Method and apparatus for making a three-dimensional object by stereolithography

ABSTRACT

An improved method for stereolithographically making an object by alternating the order in which similar sets of vectors are exposed over two or more layers. In another method, a pattern of tightly packed hexagonal tiles are drawn. Each tile is isolated from its neighboring tiles by specifying breaks of unexposed material between the tiles. Using an interrupted scan method, vectors are drawn with periodic breaks along their lengths. In another method, modulator and scanning techniques are used to reduce exposure problems associated with the acceleration and deceleration of the scanning system when jumping between vectors or changing scanning directions. In another method, a capability for automatically inserting vents an drains into a three-dimensional object representation is provided.

This is a continuation of U.S. patent application Ser. No. 08/428,950,filed on Apr. 25, 1995, now abandoned. This patent application isincorporated herein by reference as if set forth in full.

BACKGROUND OF THE INVENTION Field of the Invention

This invention relates to the field of stereolithography, which is atechnique for making solid, three-dimensional objects (or "parts") fromsolidifiable materials (e.g. fluid or fluid-like material such asphotopolymers, sinterable powders, and bindable powders).

In recent years, stereolithography systems, such as those described inU.S. Pat. No. 4,575,330, issued Mar. 11, 1986 and entitled "Apparatusfor Production of Three-Dimensional Objects by Stereolithography," havecome into use. Basically, stereolithography is a method forautomatically building complex three-dimensional parts by successivelysolidifying thin cross-sectional layers. These layers may be composed ofphotopolymer resin, powdered materials, or the like. Some types ofpowder materials are converted from a fluid-like medium to a cohesivecross-section by melting and solidification. The layers are solidifiedon top of each other consecutively until all of the thin layers arejoined together to form a whole part. Photocurable polymers change fromliquid to solid upon exposure to synergistic stimulation. Manyphotopolymers exist whose photospeed (rate of transformation from liquidto solid) upon irradiation with ultraviolet light (UV) is fast enough tomake them practical model building materials. In a preferred system, aradiation source (e.g., an ultraviolet laser) generates a beam which isfocused to a small intense spot which is moved across the liquidphotopolymer surface by galvanometer or servo type mirror x-y scanners.The scanners are driven by computer generated vectors or the like. Thematerial that is not polymerized when a part is made is stillfunctionable and remains in the vat for use as successive parts aremade. With this technology, the parts are literally grown from a vat offluid-like material (e.g. resin or powder). Specifically, the parts aregrown from a thin layer near a surface of the vat of fluid-likematerial. In this manner precise complex three dimensional patterns canbe rapidly produced. This method of fabrication is extremely powerfulfor quickly reducing design ideas to physical form for makingprototypes.

This technology typically utilizes a stereolithography apparatus,referred to as an "SLA," which generally includes a laser and scanner, aphotopolymer vat, an elevator, and a controlling computer. The SLA isprogrammed to automatically make a three-dimensional part by forming itas a sequence of built-up cross-sectional layers.

Stereolithography represents an unprecedented way to quickly makecomplex or simple parts without tooling. Since this technology dependson using a computer to generate its cross-sectional patterns, there is anatural data link to computer aided design and manufacture (CAD/CAM).However, such systems have presented challenges relating to structuralstress, shrink-age, curl and other distortions, as well as resolution,speed, accuracy and difficulties in producing certain object shapes.

The techniques to be described herein are also useful in other SolidModeling, or Rapid Prototyping and Manufacturing, technologies. One ofthese other technologies builds up objects from sheets of materials, asdescribed in U.S. patent application Ser. No. 07/803,681, now U.S. Pat.No. 5,182,715. In some embodiments these sheets of material aretransformed upon exposure to appropriate radiation, which transformationcan benefit from the techniques to be described herein.

Related Patents and Applications

The following patents and patent applications are incorporated byreference into this disclosure as though fully set forth herein:

U.S. Pat. No. 5,130,064 describes some methods of practicingstereolithography involving continuous skinning and weave patterns. U.S.Pat. No. 5,184,307 describes in great detail the presently preferredstereolithographic apparatus, as well as various methods to form partstherewith. This application is incorporated herein by reference,including its appendices, as though fully set forth herein to facilitatehandling due to its relatively lengthy disclosure. Two referencemanuals, The SLA-250 User Reference Manual and The SLA-500 ReferenceManual are hereby incorporated into this disclosure by reference asthough fully set forth herein. These manuals accompanied U.S. patentapplication Ser. No. 429,435 (now U.S. Pat. No. 5,130,064) as AppendicesB and C respectively.

U.S. Pat. No. 4,575,330 to Hull discusses stereolithography in general.It teaches complete polymerization of each cross-section in theformation of a stereolithographically-formed object.

U.S. Pat. No. 5,076,974, and U.S. patent application Ser. No.07/415,134, now abandoned, describe off-absorption-peak wavelength postcuring of parts which were formed based on the primary approach tobuilding stereolithographic parts.

U.S. Pat. No. 5,104,592 describes several methods of reducing curldistortion.

U.S. Pat. No. 4,999,143 describes the use of web supports to support andminimize curl in a part being formed.

U.S. Pat. No. 5,015,424 describes the use of "smalleys" to minimizecurl.

U.S. Pat. No. 5,182,056 describes the use of multiple penetration depthsin the stereolithographic process, along with the use of beam profilecharacteristics in combination with resin parameters to predict variouscure parameters associated with the creation of stereolithographicparts. This application also describes the role of beam profileinformation in the creation of skin fill and discusses various multiplewavelength curing methods for reducing part distortion.

U.S. patent application Ser. Nos. 07/415,168, 07/268,428, and07/183,012, all of which are now abandoned, and U.S. Pat. No. 5,234,636,disclose various methods of finishing a stereolithographic part surfaceto smooth out discontinuities in a post-processing step.

U.S. patent application Ser. Nos. 07/265,039, which is now abandoned,and 07/249,399 which together form the basis of PCT Application Ser. No.PCT/US89/04096, WIPO Publication No. WO 90/03255, disclose the use of adoctor blade for obtaining a uniform coating of resin of known thicknessover each cross-section of a stereolithographic part as well as a systemfor maintaining a known surface level of the building material as thepart is being built.

U.S. patent application Ser. No. 07/429,301 discusses post-processingtechniques.

In the normal practice of stereolithography, objects or "parts" arebuilt on a layer-by-layer basis, where each layer represents a thincross-section of the part to be formed. Initial approaches tostereolithographic part building were based on the complete filling(e.g. substantial polymerization of all regions of a cross-section to athickness at least as deep as the layer thickness) of layers. Thisfilling was either done by the scanning of a pencil of light, by afocused or defocused pencil of light, or by flood exposure of anappropriate cross-sectional image. The pencil of light approach strictlyused complete filling of cross-sections based on the scanning ofadjacent overlapping vectors until the entire cross-sectional patternwas cured. These initial approaches suffered from several drawbacks,including distortion, curl, inaccurate sizing, lack of structuralintegrity, and lack of uniformity in down-facing surface appearance.

Later stereolithographic techniques used an internal lattice ofpartially cured building material ("cross-hatch" or "hatch") in place ofcompletely filling the successive cross-sections. The internalstructures primarily consisted of cross-hatch separated by untransformedbuilding material (e.g. liquid photopolymer or the like). In thisapproach, the outer and inner edges of each layer are solidified byscanning of what are called "boundary vectors" (also termed,"boundaries" or "border vectors" or "borders"). These vectors separatethe interior cross-hatched regions of a cross-section from exterioruntransformed building material. Cross-sections or portions ofcross-sections that bound external regions of the part are completelyfilled with skin fill (termed "fill" or "skin") after beingcross-hatched. The hatch ensures adequate support for the "skin" as itis being created, thereby minimizing distortion.

The skin, crosshatch, and borders trap untransformed building material(e.g. liquid photopolymer) internally in the part structure and hold itin place while the part is being created. The trapped untransformedbuilding material (e.g. liquid photopolymer) and at least partiallytransformed building material (e.g. at least partially cured polymer)which forms the boundaries, hatch, and skin are brought to fulltransformation (e.g. polymerization) in a later process known as "postcuring". For additional information on post-curing, see U.S. patentapplication Ser. No. 07/415,134.

Fairly extensive post-curing can be required when the internalcross-hatch lattice only defines discrete x-z and y-z, planes, or thelike, which are separated from each other by more than the width curedby a beam, as in such cases long vertical corridors of unpolymerizedmaterial remain substantially uncured until post-processing. It is anobject of the invention to provide a method of reducing or eliminatingpost-processing time and associated distortions while increasingstructural integrity of the stereolithographically formed part.

Stereolithographic building techniques have upon occasion resulted indown-facing features having a "wafflish" appearance and texture. Thisappearance and texture are due to inappropriate curing techniques beingused on regions of layers that contain down-facing features. Whendown-facing features are given both hatch and skin fill, there can beoverexposure of the regions where the hatch and fill coincide.Similarly, overexposure can occur at the points of intersection ofcross-hatch vectors. In the past, it has been possible to ignore therequirement of uniform cure depth for down-facing features, since otheraccuracy-related errors overshadowed this effect. However, as thestereolithography art strives for and attains increasingly higher levelsof accuracy, imperfections such as these can no longer be overlooked. Itis an object of the invention to correct these imperfections incombination with improved building techniques.

It is also an object of the invention to obtain accurate skinthicknesses without the need of periodically building test parts andwithout the need of being concerned with energy distribution in the beam(beam profile). Traditionally, the methods used to estimate skin depthwere only guesses that had a remote connection to actual experimentaldata or theoretical expectations. The actual skin thicknesses obtainedby these traditional approaches were strongly dependent upon beamprofile characteristics, skin vector spacing, drawing speed, and resincharacteristics. However, these parameters were not coordinated to yielda particular skin thickness. For example, skin thicknesses intended tobe 20 mils could easily range from 15 to 25 mils. In the past, this typeof thickness range has been tolerated, but as the art ofstereolithography advances, there is an increasing need for moreaccurate and less cumbersome methods of predicting the required exposureto obtain a desired skin thickness.

It is a further object of the subject invention to provide a method forautomatically placing vents and drains in a three-dimensional objectrepresentation such that unsolidified material is able to drain from theobject after it is built through stereolithography.

SUMMARY OF THE INVENTION

To these ends, a stereolithographic method comprises the steps ofconstructing stacked layers to form an object having externalboundaries, internal cross hatch, and skinned up- and down-facingfeatures. Skin fill is provided in less than all regions of the stackedlayers, but in association with more than the up- and down-facingfeatures of the object.

To these ends, all cross-sectional layers may be provided with skin filland crosshatch.

According to another aspect of the invention, a method provides allcross-sectional layers with boundaries and unidirectional fill ormultidirectional fill and no cross hatch.

According to another aspect of the invention, a method providesboundaries appropriate to each cross-section and provides cross-sectionswith at least two types of non-parallel hatch vectors wherein effectiveadhesion (that capable of transmitting significant curl) only occurs atthe overlapping points between the vectors of the two hatch types.Additionally the hatch vectors of each type are spaced as close togetheras possible without being spaced so close that they can induce curl intoadjacent vectors or have curl induced in them by adjacent vectors.

According to another aspect of the invention, a method comprises thesteps of providing boundaries appropriate to each cross-section andproviding cross-sections with at least two types of non-parallel hatchvectors that are offset from their corresponding types on the previouslayer wherein effective adhesion between cross-sections (that capable oftransmitting significant curl) only occurs near the overlapping pointsbetween the vectors of the two hatch types of the present layer.Additionally, the hatch vectors of each type are spaced as closetogether as possible without being spaced so close that they can inducecurl into or have curl induced in them by adjacent vectors or transmitcurl from one vector to another vector.

According to another aspect of the invention, each region of across-section that is internal to the object (i.e. not forming adown-facing or up-facing region), is cured in the form of pointexposures, "bullets". The point exposures on successive layers areoffset one from another, and the bullets are cured to approximately adepth of one layer thickness. The spacing of the point exposures on asingle layer are as close together as is reasonable without the materialcured in association with each bullet affecting the material cured inassociation with adjacent bullets. In this approach the up-facing anddown-facing features may be formed by a variety of techniques.

According to yet another aspect of the invention, each region of across-section that is internal to the object (i.e. not forming adown-facing or up-facing region), is cured in the form of pointexposures, "bullets", wherein the bullets are cured to a depthsubstantially equal to two layer thicknesses, and wherein bullets onsuccessive layers are offset one from another. The positioning patternis repeated every other layer, and the spacing of the bullets on eachcross-section is such that their cured separation is greater than zerobut less than their cure width one layer thickness below their uppersurface. The bullets cured on the present layer substantially fill inthe gaps left in the previous cross-section when it was formed. In thisapproach the up-facing and down-facing features may be formed by avariety of techniques.

According to another aspect of the invention, each region of across-section that is internal to the object and exists on the presentcross-section as well as the N-1 succeeding cross-sections, is cured inthe form of point exposures, "bullets". Each cross-section is dividedinto a pattern of slightly overlapping bullets. These bullets aredivided up into N groups where the bullets associated with successivegroups are used to expose material in association with the successivecross-sections beginning with the present cross-section. Each bullet iscured to a depth substantially equal to N layer thicknesses. In thisapproach, regions of cross-sections within N-2 layers of a down-facingfeature are handled by modified techniques similar to those describedabove, and the up-facing and down-facing features may be formed by avariety of techniques.

According to yet another aspect of the invention, at least up- anddown-facing features are provided with skin fill that is created byscanning in a first pass using nonconsecutive fill vectors, followed byscanning in at least one additional pass that completes the exposingprocess by filling in between the originally drawn vectors.

According to another embodiment of this invention, objects are formedwith a build style that promotes the draining of untransformed buildingmaterial from the internal portions of it. The objects producedaccording to these techniques have particular usefulness as investmentcasting patterns. The ability of the untransformed building material tobe removed from the internal portions of the object is a result of usingwide spaced hatch patterns that are periodically offset and/or using atleast some hatching patterns that result in broken lines of transformedmaterial. Multiple skins and/or multiple boundaries may also be used.Furthermore, more complex embodiments are possible that use differentbuilding parameters for different internal portions of the object. Someof these more complex embodiments use minimal internal grid structurenear the surfaces and boundaries of the object and use more internalgrid structure deep within the object. Other embodiments use some gridstructure near the surfaces and boundaries of the object but use less orno grid structure in the deep internal regions of the object.

In another aspect of the invention, regions of intersecting vectors atleast in down-facing surfaces are determined, and exposure of one ormore of the respective intersecting vectors at these intersectingregions is reduced, such that at least the down-facing features have auniform exposure.

In another aspect of the invention, a region that contains a combinationof hatch and fill vectors is created and cured to a uniform depth. Thecreation of this region comprises the steps of creating the desiredhatch vectors, and then creating corresponding skin fill types that donot contribute to additional exposure of the regions of theircorresponding hatch vectors.

In another aspect of the invention, an improved stereolithographicmethod comprises determining necessary exposure and vector spacing andscanning parameters in order to obtain a known thickness of skin fill.

In still another aspect of the invention, a stereolithographic methodcomprises the steps of constructing stacked layers to form an objecthaving external boundaries, internal cross hatch, and skinned up- anddown-facing features. Specifically, this method comprises the steps of:(a) selecting layers to be provided with skinned surfaces; (b) providingmeans for calculating the amount of total exposure required to obtainskin curing of a preselected depth at the layers selected to haveskinned surfaces; (c) providing means for determining the number ofvectors that will be exposing each region in the layers, and (d)providing means for at least partially transforming (e.g. polymerizing)the layers by exposing them first to boundary vectors, then to hatchvectors, and then to skin vectors, each vector providing an exposuresufficient to cure to the preselected depth calculated in step (b),divided by the number of other vectors that will intersect the vector ata given region as determined in step (c).

According to yet another aspect of the subject invention, a method isprovided for automatically placing vents and drains in athree-dimensional object representation such that unsolidified materialis able to flow from the object after it is built throughstereolithography in accordance with the QUICKCAST style of building.

According to other aspects of the invention, these improvements are usedin combination with one another and/or in combination with curlreduction techniques as described in: U.S. Pat. No. 5,104,592; U.S. Pat.No. 5,015,424; U.S. Pat. No. 4,999,143, and the other patents and patentapplications cited previously all of which are fully incorporated hereinby reference. For example, according to yet another aspect of theinvention, an improved stereolithographic method is disclosed comprisingthe combined use of hatch with nonconsecutive skin fill in more than theup- and down-facing features. As another example, an improvedstereolithographic method is disclosed comprising the method of reducingexposure where vectors intersect and providing discontinuities in skinfill to avoid multiple vector exposure in regions where hatch vectorshave been provided.

Another aspect of this invention provides apparatus which are used toimplement the methods discussed above either singly or in combination.

Other aspects of the invention, together with objects and attendantadvantages of the various embodiments, will best be understood from anexamination of the drawings along with the detailed description below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1a-1d collectively show a top view of a layer showing boundaries,hatch and skin without compensation for multiple exposures of buildingmaterial at the various regions of the cross-section. FIGS. 1a-1drepresent respectively: a) boundaries only; b) crosshatch only; c) skinonly; and d) combined vectors.

FIGS. 2b-2d collectively show side views of FIG. 1d as intersected byvarious vertical planes identified in FIG. 2a. FIGS. 2a-2d represent,respectively: a) repeat of FIG. 1d with vertical planes; b) a view ofthe edge of the layer along plane 1 showing the various depths obtainedin different regions; c) a view of the edge of the layer along plane 2showing the various depths obtained in different regions; and d) a viewof the edge of the layer along plane 3 showing the various depthsobtained in different regions.

FIGS. 3a-3e collectively illustrate a top view of a layer showingboundaries, hatch and skin as created by a presently preferredtechnique. FIGS. 3a-3e represent respectively: a) boundaries only; b)crosshatch only; c) skin type 1; d) skin type 2; and e) combinedvectors.

FIGS. 4b-4d collectively show side views of FIG. 3e as intersected bythree different vertical planes identified in FIG. 4a. FIGS. 4a-4drepresent, respectively: a) repeat of FIG. 3e with vertical planes; b) aview of the edge of the layer along plane 1 showing the various depthsobtained in different regions; c) a view of the edge of the layer alongplane 2 showing the various depths obtained in different regions; and d)a view of the edge of the layer along plane 3 showing the various depthsobtained in different regions.

FIGS. 5a and 5b illustrate the profiles of a cured "string,"corresponding to the cure produced by a single vector.

FIGS. 6a-6d show down-facing surface profiles of parts made inaccordance with Example II below.

FIGS. 7a-7c show a comparison between traditional vector orderingtechniques and examples of various vector ordering techniques of some ofthe preferred embodiments of the present invention. FIG. 7a depicts atop view of a cross-section of an object showing a consecutive drawingorder for the vectors. FIG. 7b depicts the same cross-section but filledusing a non-consecutive order that fills the cross-section in twopasses. FIG. 7c depicts the same cross-section but filled using anon-consecutive order that fills the cross-section in three passes.

FIGS. 8a-8i collectively illustrate the vectors used and cure depthsobtained, for a sample cross-section, by utilizing the "weave" buildingembodiment. FIGS. 8a, 8c, and 8e respectively represent top views ofboundary vectors, X hatch vectors, and Y hatch vectors. FIGS. 8b, 8d,and 8f depict side views of the material cured in association with FIGS.8a, 8c, and 8e respectively. FIG. 8g represents a top view of thecombination of material cured by the individual vector types of FIGS.8a, 8c, and 8e. FIGS. 8h and 8i represent side view of the cure depthsassociated with two different vertical planes intersecting thecross-section of FIG. 8g.

FIGS. 9a and 9b collectively show a side view indicating the differencebetween stacking one direction of crosshatch on top of each other fromlayer to layer and staggering the hatch from layer to layer. FIG. 9adepicts a side view of hatch being stacked on top of each other fromlayer to layer. FIG. 9b depicts a side view of hatch being staggeredfrom layer to layer.

FIGS. 10a-10c collectively show the configuration of bullets cured inassociation with practicing the seventh embodiment of the presentinvention. FIG. 10a depicts a top view of the boundary and bullets curedon a first cross-section. FIG. 10b depicts a top view of the boundaryand bullets cured on a second cross-section. Comparison of FIGS. 10a and10b indicate that the bullets are staggered from the first to the secondlayer. FIG. 10c depicts a side view of the boundaries and bullets offive cross sections stacked one on top of the other.

FIG. 11 illustrates a side view of the overlapping nature of the bulletsformed in practicing the eighth embodiment of the present invention.

FIG. 12 depicts the three-dimensional object used in Example 1 to testthe improvements of "skintinuous" building.

FIG. 13 depicts a top view of the uppermost cross-section of the part ofFIG. 12, along with indications as to what measurements were made on thepart; and

FIGS. 14a and 14b collectively depict a side view of a CAD designedobject and the object as reproduced according to the teaching of thefirst preferred embodiment of the present invention. FIG. 14a depictsthe CAD designed object, and FIG. 14b depicts the reproduction.

FIGS. 15a, 15b, and 15c collectively depict the part used in theexperiment of Example VI. FIG. 15a depicts a three-dimensional view ofthe part. FIG. 15b depicts a top view of the part. FIG. 15c depicts anexaggerated top view of the distortion of the part after post curing.

FIGS. 16a, 16b, and 16c collectively depict sample cross-sections of anobject for the purpose of distinguishing up-facing and down-facingfeatures of an object and the relationship of such features tosubregions of each cross-section. FIG. 16a depicts a top view of thebounded and unbounded regions of a single sample cross-section. FIG. 16bdepicts a side view of three sample cross-sections of an object. FIG.16c depicts a side view of the subregions of the middle cross-section.

FIGS. 17a-g illustrate various patterns and shapes for tiling and theweak bending axes, if any, associated with each pattern/shapecombination.

FIGS. 18a and 18b are top views of vectors scanned respectivelyaccording to a first pass of an offset weave square tiled exposurepattern and according to both passes of an offset weave square tiledexposure pattern.

FIGS. 19a, 19b, and 19c are top views of vectors scanned respectivelyaccording to a first pass of an offset-weave hexagonal-tiled exposurepattern and according to both passes of an offset-weave hexagonal-tiledexposure pattern and according to both passes of an alternativeoffset-weave hexagonal-tiled exposure pattern.

FIG. 20 depicts the currently utilized conventional scanning order forfill and hatch vectors.

FIGS. 21a and 21d depict respectively each of the scanning patterns of afour-layer sequence of cross-sections utilizing the drawing order ofalternate sequencing example #2.

FIGS. 22a to 22h depict respectively each of the scanning patterns foran eight-layer sequence of cross-sections utilizing the drawing order ofalternate sequencing example #3.

FIGS. 23a, 23b, and 23c depict the gaps between tiling on a first layerbeing filled in on a second layer with slightly offset tiles followed bygrouting between the offset tiles.

FIG. 24 depicts closing gaps between tiles on a first layer with an atleast partially floating member on a second layer which floating portionis riveted to an adjacent tile on the first layer.

FIGS. 25a to 25g depict various orientations of vectors n and n+1 alongwith various virtual scanning paths that can be followed to scan fromvector n to vector n+1.

FIGS. 26a and 26b depict two cross-sections of an object wherein eachcross-section uses a different hatching pattern.

FIGS. 26c and 26d depict vertical cuts through the object of FIGS. 26aand 26b at the two locations indicated.

FIG. 27 depicts a cross-section divided into two regions with eachregion being hatched with a different pattern.

FIG. 28 depicts a flowchart of the process of inserting a vent into apart through VIEW.

FIG. 29 depicts a flowchart of the process of inserting a drain into apart through VIEW.

FIG. 30 illustrates the "Vents and Drains" window of VIEW.

FIGS. 31-33 & 35 illustrates various perspective views of an object intowhich has been inserted vents and drains.

FIG. 34 illustrates the "Viewing Transformation" window of VIEW.

FIG. 36 illustrates the use of a Boolean operation to insert avent/drain in a flat region.

FIG. 37 illustrates the case in which the vent/drain extends beyond aflat region.

FIGS. 38-39 illustrate a first approach for inserting a vent/drain in anear-flat region.

FIGS. 40a-40c illustrate a second approach for inserting a vent/drain ina near-flat region.

FIGS. 41a-41b illustrate a problem that can occur with this approach inrelation to steep near-flat regions.

FIG. 42 illustrates the creation of unwanted hatch/fill that occurs whenportions of layer boundaries are eliminated.

FIGS. 43a-43b illustrate the use of a plurality of lines spaced in thez-direction to represent a vent/drain on a near-flat or verticalsurface.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The instant invention addresses alone or in combination fourimprovements in stereolithographic methods. These are, first: methods ofincreasing structural integrity while reducing the need for post-curing;second: methods of obtaining uniform exposure in regions of intersectingvectors of different types; third: methods of determining cure depth;and fourth: methods intended to reduce distortion due to shrinkage,curl, and post cure. Although these four aspects of the invention areclosely inter-related and are often cross-dependent, they will beaddressed in sequence in this detailed description, and will also beillustrated in the examples below.

Definitions

"Beam profiles" represent the energy distribution of irradiation in abeam of ultraviolet light or the like, used to cure photopolymer orother curable material in accordance with stereolithography practices.

"Building materials" are materials that can be used in the presentinvention for forming three-dimensional parts. The acceptable buildingmaterials are materials that can transform from one state to anotherstate in response to exposure to synergistic stimulation. The two statesare then separable after exposure of a single layer to synergisticstimulation or separable after completion of a plurality of layers. Themost preferred materials are materials that transform from a fluid-likestate to a cohesive state or solid state. These materials include liquidphotopolymers, sinterable powders, bindable powders or the like. Priorto exposure to appropriate synergistic stimulation (e.g. IR radiationfrom a Carbon Dioxide laser or the like) the sinterable powders are in afluid-like state since the powder particles can flow past one anotherwhereas after sintering the powder particles are joined to form acohesive mass. Similarly the bindable powders are in a fluid-like stateprior to exposure to appropriate synergistic stimulation (e.g. achemical binder dispensed into the powder in a selective and controlledmanner) whereas after exposure the binder sets and the powder (andbinder) form a cohesive mass. The most preferred of the above materialsfor the present invention are the photopolymer type materials. Otheracceptable materials include relatively solid sheets of material thatare transformable from one state to another. These sheet like materialsinclude "dry film" type photopolymer materials that can be solidifiedupon exposure to appropriate synergistic stimulation wherein afterexposure the exposed and unexposed materials can be separated bydifferential solubility in an appropriate solvent.

"Bullets" are volumes of a building material which are solidified inresponse to a beam of synergistic stimulation exposing the material insubstantially single non-overlapping point irradiations. The usual shapeof the cured material is similar to that of a bullet. FIG. 5b depicts across-sectional view of a line or vector of material cured by a beam ofradiation. It can equally well be interpreted as depicting a twodimensional view of a bullet, wherein the three-dimensional bullet wouldbe the volume of revolution formed by rotating the object about avertical axis through its center.

"Effective Cure Width" (ECW) is a distance equal to twice the closestpossible spacing of two vectors from one another that will render agiven individual cure depth (i.e., a cure depth associated with eachvector) without measurably increasing the cure depth of the combination.For the preferred beam profiles and cures, the Effective Cure Width(ECW) is always less than the Maximum Cure Width (MCW) (i.e., the widthof the solidified string at the building material surface), such thatdifferent lines of solidified material can be adhered without anincrease in cure depth. For example, in FIG. 5b, the horizontalseparation between lines 118 and 120 might represent the ECW for string100. Typically, one half the ECW represents the closest point that asimilar line of material can approach string 100 without measurablyincreasing its maximum cure depth. More generally, the ECW is a zonethat surrounds the center line of a string, such as string 100, thatrepresents the closest position that another string (of arbitrarythickness and direction) of solidified material or set of strings ofmaterial can approach the first string without resulting in the maximumcure thickness of the combination being measurably greater than themaximum thickness of either string. As two non-parallel vectors approachan intersection point, the excess exposure point, "EEP" (the point atwhich the combination will cause a measurable increase in cure depth) isdetermined by the beam profile and angle of approach of the two vectors.If the vectors are perpendicular the excess exposure point is the 1/2the ECW. If the vectors approach each other at a 45 degree angle theexcess exposure point is at 1/2×1.414×ECW. An approximate relationshipbetween ECW, the angle of approach, and the EEP is

    EEP=(1/2)×ECW/SIN(A),

where A is the angle between the vectors. A more accurate relationshipcan be derived from information regarding the beam profile, the depth ofcure, the building material response characteristics, and theintersection direction of the vectors.

"Layers" are the incremental thicknesses between successivecross-sections into which an object is divided. These layers form thebasis for the thicknesses of building material (e.g. photopolymer). Theymust receive sufficient exposure to synergistic stimulation (e.g.ultraviolet light or other polymerizing radiation) to transform fromtheir fluid-like state into a cohesive structure. The layers areconstructed to adhere to one another and collectively form a solidified(e.g. polymerized or partially polymerized) stereolithographicallyproduced part.

"Maximum Cure Depth (MCD)" and "Maximum Cure Width (MCW)" refer,respectively, to the deepest and widest cure that is obtained whenexposing a single line or bullet of uncured building material tosynergistic stimulation. The maximum cure depth is generally what isreferred to as the cure depth of boundary and hatch lines. Since a beamof light is not generally of constant intensity across its width, thecure depth and width caused by a beam tracing across a line one or moretimes does not produce a uniform depth and width of cure. The maximumdepth of cure generally occurs near the middle of a cross-section of thetrace but it can actually occur anywhere depending on the distributionof intensity in the beam. It may also depend on the direction ofscanning of the beam in forming the trace. The maximum width of curegenerally occurs at the top (surface) of the cured line of material. Anexample of the maximum depth and width of cure are depicted in FIG. 5awhich shows a line (sometimes called a string) of cure material 100.Vector 102 indicates the scanning direction used in creating the stringof material 100. Surface 104 represents the solidified material that wascreated from the fluid-like material that formed part of the surface ofthe curable material. FIG. 5b represents an end-on view of string 100.Line 106 indicates the position of the top of the cured string 100,while line 108 represents the bottom of cured string. The verticaldistance between 106 and 108 is the maximum cure depth of string 100.Line 112 represents the left-most edge of string 100, while line 114represents the right-most edge of string 100. The horizontal separationbetween 112 and 114 is the maximum cure width of string 100. Such astring 100 of solidified building material may be used for severalpurposes: 1) to insure adhesion between the layer associated with itscreation and the preceding layer, 2) to form a down-facing feature of apart being created, or 3) as an element of a series of such strings ofcured material, where the series will be used for one of the above twopurposes. An up-facing feature is not included in the above since it canbe fit into one of the above categories depending on the situation. Forthe first purpose listed above, maximum cure depth may preferably begreater than the layer thickness. The vertical separation between line106 and line 110 represents the layer thickness in such a case. For thesecond purpose the MCD represents the layer thickness, and for the thirdpurpose the vertical separation between line 106 and line 116 mightrepresent the layer thickness since the net thickness of the curedmaterial might increase from the segments overlapping each other.

"Overlapping" refers to two or more exposures being given to a region sothat an increase in maximum cure depth occurs. Since cure profiles arenot necessarily step functions, two separately exposed areas can touchand bind to one another without changing the maximum cure depth ofeither. When two lines are exposed beside one another their maximumwidths may overlap resulting in a larger exposure in this region, and acorresponding increase in depth. But if this additional exposure doesnot occur in the region near the maximum cure depth of the individuallines, their combined maximum cure depth will not generally bemeasurably deeper than their individual maxima. Overlapping sometimesrefers to situations when two side by side exposures affect the curingof each other whether or not they result in an increase in the maximumcure depth of either one. The context in which the term "overlapping" isused will generally make its meaning clear.

"QUICKCAST" is any of a number of different building styles which allowuntransformed material to be removed from the interior of the walls ofthe object after formation. The ability of the untransformed buildingmaterial to be removed from the internal portions of the object is aresult of using wide spaced hatch patterns that are periodically offsetand/or using at least some hatching patterns that result in broken linesof transformed material. Multiple skins and/or multiple boundaries mayalso be used. The drained objects are typically used as investmentcasting patterns. Since these build styles produce objects with littledistortion and since they also use relatively small amounts of buildingmaterial, they are considered practical building styles for manyapplications.

"Step Period" (SP) is a part-building parameter that defines the periodof time between each laser step.

"Step Size" (SS) is a part-building parameter that defines the spatialsize of the step moved by the laser spot on the building materialsurface.

"Vectors" are data that represent the length and the direction and maybethe period of irradiation (exposure) in the process of solidifying thebuilding material in the preferred embodiment of the present invention(e.g. a scanning beam of ultraviolet radiation, on a liquidphotopolymer, or other fluid-like solidifiable medium).

"Skin" vectors are horizontal surface vectors that are typically tracedfrom one boundary to an opposing boundary at relatively high speed andwith a substantial overlap between successive vectors which aregenerally traced in opposite directions, and typically form "skin fill"which defines at least the upper and lower horizontal exterior surfacesof a stereolithographically-formed part in traditional stereolithographyand in several of the preferred embodiments of the present invention.Typically, skin vector spacing is from about 1 to about 4 mils with amaximum cure width of a single exposed skin vector being about 14 to 15mils. Of course, these exemplary and illustrative parameters can bevaried as needed based upon such considerations as the desiredsmoothness of the layers, the power of the laser, the possible speedrange of the irradiating source (i.e., the maximum drawing speed), thelayer thickness desired, and the number of vectors that are desired tobe stored. According to certain aspects of this invention, however, skinfill is provided in more than the exterior surfaces of the part.According to other aspects of the invention, skin vectors can be drawnnon-consecutively and/or nonoverlapping (e.g., a first pass at 7-8 milintervals and a subsequent pass at intervening intervals). These aspectsand others are described in detail below.

"Boundary" vectors are traced to define the vertical exterior surfacesof the stereolithographically-formed part (therefore to define the rangeof each cross-section). These vectors generally are scanned more slowlythan skin vectors such that a greater cure depth is obtained.Boundaries, unlike skin fill, generally do not rely on overlappingoffset passes to attain their full cure depth. In situations whereregions on a given layer overlap regions of the previously formed layer(non-down-facing regions), it is preferred that the cure depth exceedthe layer thickness, so that improved adhesion between layers results.In regions of down facing features, it is preferred that net cure depthbe substantially equal to the layer thickness.

"Hatch" vectors are similar to boundary vectors, except that they aretraced in a substantially uniform, criss-cross type pattern, to definethe internal lattice structure of the stereolithographically-formedpart. Again, it is preferred that the cure depth exceed the layerthickness, if being drawn in a non-down-facing region, so that improvedadhesion between layers results. If being drawn in a down-facing region,then layer thickness cure depth is preferred. In several preferredembodiments of the present invention, adhesion between layers isobtained by the extra cure depth that is obtained from the intersectionsof two or more crosshatch vectors wherein the cure depth of theindividual hatch lines is insufficient to cause curl inducing adhesionbetween the layers.

"Skintinuous" in general terms describes any building technique whichgenerates a substantially solid fill pattern over a substantial portionof the cross-sectional area of a part.

"Multipass" refers to a drawing technique which utilizes more than onepass to expose a region (e.g. a line) so that the material issubstantially reacted before direct adhesion with surrounding structurestakes place. The purpose of this method is to minimize pulling forcesbetween layers and therefore to reduce curl.

"Interrupted Scan" or "Bricking" refers to scanning a vector withrecurring gaps to relieve transmitted stress.

"Tiling" is an interrupted scanning technique that applies to relativelywide regions as opposed to vectors (the wide regions may be made up ofvectors). This scanning results in distinct shapes which fit togethervery snugly but are not adhered to each other. The intention of thismethod is to maximize percentage of build process curing while reducingtransmitted stresses that generate curl.

"Log Jam" refers to a scanning technique where some internal hatch (orfill) vectors are retracted from the layer borders to avoid adhesion,wherein after exposure of the hatch or fill an offset border or the likeis scanned to attach the hatch and original border.

"Quilting" refers to a drawing technique which first partitions eachlayer into patches by scanning a relatively large crosshatch structure.Each patch is then treated as an individual region to be scanned. Thismethod relieves problems that can arise when drawing relatively largeregions with floating material techniques (e.g. log jam).

"Strongarm" refers to a scanning technique wherein a downfacing regionis given extra exposure to make it extra rigid thereby increasing itsability to resist distortion caused by adhesion with material from thenext higher layer.

"Weave" generally refers to any drawing pattern which generates a nearsolid fill pattern, wherein vectors on the first pass (threads) arespaced slightly further apart than the maximum cure width (MCW) and haveexposures that are less than that necessary for adhesion (i.e. undercured). Adhesion is obtained on a second pass or higher order pass bycumulative exposure resulting at the intersecting regions of threads.These intersecting regions are sometimes called stitches.

"Interlace" is a particular type of "non-consecutive scanning" whereinevery other vector is scanned on a first pass of a region and the othervectors are scanned on a second pass.

"Staggered" refers to a building method where different drawing patternsare used on alternating layers. For example staggered hatch refers tooffsetting or shifting the hatch vectors on every other layer so thatthe hatch vectors on adjacent layers do not overlay each other. Theintended purpose of this method is to produce a more homogeneousstructure and possibly to reduce curl in some instances.

"Smalleys" refer to a building technique where holes or gaps are placedat critical locations on a given cross-section (generally implementedthrough the CAD design but they can be implemented from a Slice typeprogram onto individual cross-sections). They reduce curling byinterrupting the propagation of stresses from one region of a layer toanother region of the layer.

"Riveting" or "Stitching" refers to an exposure technique that appliesdifferent levels of exposure to a given layer, wherein some of theexposures are less than that necessary for adhesion and some of theexposures are sufficient to cause adhesion thereby creating discretelocations of adhesion which might resemble rivets.

"Webs" are support structures that are not a portion of a desired finalreproduction of a CAD designed object but they are formed along with theobject by the stereolithography apparatus to give support to variousfeatures of the object and to allow easy separation of the object fromthe building platform.

"Up-facing and Down-facing Features of an Object" are regions orsubregions on particular cross-sections that represent an upper or lowerextent of the object.

Each cross-section is formed from a combination of bounded and unboundedregions. Bounded regions are those that form a portion of the solidstructure of an object (regardless of whether the region is formed as acompletely solidified region or as a cross-hatched region). Unboundedregions are those that form an empty or hollow portion of an object.These concepts are depicted in the example of FIG. 16a. FIG. 16a depictsa top view of a sample cross-section of an object. This samplecross-section can be divided into three bounded regions and twounbounded regions. Boundary 700 bounds region 705, boundary 710 boundsregion 715, and boundary 720 and 725 bound region 730. Regions 735 and740 are unbounded regions.

Each of the bounded regions of a cross-section may be divided intosubregions, which are determined by relationships between boundedregions on a given cross-section and bounded and unbounded regions onthe two adjacent (one higher and one lower) cross-sections. Up-facingregions of cross-section "I" are those bounded subregions ofcross-section "I" that are underneath unbounded subregions ofcross-section "I+1". The down-facing subregions of cross-section "I" arethe bounded subregions of cross-section "I" which overlay unboundedsubregions of cross-section "I-1". Some subregions may represent bothup-facing and down-facing features; in this case the subregion isgenerally considered to be a down-facing subregion since appropriatecuring of down-facing features is generally more critical than curing ofup-facing features. This concept is depicted in the example of FIG. 16band 16c. Cross-section "I", 750, is above cross-section "I-1", 755, andis below cross-section "I+1", 760. FIG. 16c is a repeat of FIG. 16b butwith cross-section "I", 750, divided into subregions. The up-facingbounded subregions of cross-section "I" are labeled as 761, 764 and 768.The down-facing bounded subregions of cross-section "I" are 761, 762,and 769. The bounded subregions that are neither up-facing nordown-facing are 763, 765, and 767. The unbounded regions ofcross-section "I" are subregions 766 and 770. It can be seen thatsubregion 761 is both up-facing and down-facing and thus it wouldgenerally be processed as a down-facing feature. If a cross-section "j"is above a completely unbounded cross-section, then all of cross-section"j" is a down-facing feature (e.g., the bottom of the part). If across-section "j" is below a completely unbounded cross-section,cross-section "j" is an up-facing feature (e.g. the top of the part).

Other definitions can be obtained as needed from remaining disclosureand the manuals attached as Appendices B and C to U.S. patentapplication Ser. No. 07/429,435 (now U.S. Pat. No. 5,130,064),incorporated herein by reference. Moreover, the specifications of theSLA hardware, the resin and laser types, and the generally preferredparameters with respect to the stereolithographic processes describedand improved upon herein are set forth in those Appendices.

Preferred Methods of Obtaining Improved Structural Integrity

Several preferred embodiments of this invention relate to methods ofobtaining improved structural integrity, lower post cure distortion,lower overall horizontal distortion, and in many cases overall lowervertical distortion (e.g. vertical curl) by effectively providing skinon more than just the up- and down-facing surfaces of the part beingformed. For example, the effect of providing skin at only the up- anddown-facing surfaces, and supplying cross hatch in x-z (X hatch) and y-z(Y hatch) planes, is to create an internal structure consistingessentially of relatively long columns of substantially untransformedmaterial trapped by at least partially transformed crosshatch andboundary material on the sides and skin on the up-facing and down-facingsurfaces. Accordingly, a leak in any portion of a down-facing orup-facing skin or cross hatch would have the potential to causedistortion and unwanted drainage of untransformed building material.However, if skin is provided in the x-y (horizontal) plane, at more thanthe up- and down-facing surfaces, then the compartments of untransformedmaterial trapped by cross-hatch, boundary, and skin would be muchsmaller and better-contained. Other advantages emanating from providingadditional skinned surfaces within the internal structure of the partcan include improved structural integrity, less distortion duringformation, reduced post-curing times, and reduced post-cure distortion.Additionally, surface finishing can be performed before post-curing, andin some circumstances, post curing can be completely avoided. There arevarious preferred embodiments that employ different approaches inobtaining this additional fill.

A first group of embodiments utilize exposures analogous to traditionalskin filling techniques in that the fill is generated by a series ofoverlapping exposures. These embodiments may or may not employ the useof what is traditionally known as cross-hatch and fill in the sameregion of a cross-section.

In a first preferred embodiment an object is formed on a layer by layerbasis initially by the exposure of building material to boundary vectorson a cross-section, followed by exposure of crosshatch vectors on thecross-section, and finally followed by exposure of skin fill vectors onany up-facing and down-facing regions on the cross-section.Additionally, on periodic or random (with a certain probability ofoccurrence) cross-sections even in non-down-facing and in non-up-facingregions skin fill vectors are provided and exposed. For example, atevery 1/2 inch vertical interval through the part, which at 10 millayers corresponds to every fifty layers, skin vectors are generatedthat provide for skinning of the entire cross-section. These skinvectors are provided in a form in which areas that are down facing canbe distinguished from areas that are not down-facing so that differentcure parameters can be used if necessary. It is possible to distinguishother regions but it has been found unnecessary to do so. The advantagesof this approach have been previously described.

Of course other vertical spacings of skin fill are possible includinggeometry selective spacing. That is some geometric features may bebetter handled by one spacing of skins while others require a differentspacing of skins. In this embodiment the boundary vectors and crosshatchvectors that are used to achieve adhesion between layers are generallygiven some overcure to insure adequate adhesion. However, the skinvectors that are used in non-downfacing regions can be given a curedepth that is less than, equal to, or greater than the layer thickness.It has generally been found that a skin depth greater than the layerthickness causes excessive curl and therefore isn't optimal. The skinvectors (combined with all other vector types) in a down facing regionare, on the other hand given, only a one layer thickness cure depth.This embodiment can be combined in all, or in part, with the uniformskin thickness methods to be described hereinafter.

This method of building can be substantially implemented by Slicing thedesired CAD object file, or the like, twice and then editing and Mergingthe resulting .sli files together. The first Slice is done with normalSlicing parameters. For example by using X and 60/120 crosshatch with a50 mil spacing and using X skin fill with a 3 mil spacing. The secondSlice is done without the use of skin fill but with the use of closelyspaced crosshatch (which will function as skin fill) of type and spacingequivalent to the skin spacing of the first Slice. For example,continuing with the previous example, the second Slice would be donewith the same layer thickness but with only X type crosshatch spaced at3 mils. After creation of the second Slice file, it is edited by hand orby a program that can go in and remove the skinning cross-hatchassociated with the cross-sections not using fill in the non-down-facingand non-up-facing regions. Next the two files are Merged together usingmerging options that keep all the vectors from the first Slice and thatkeep only the remaining X layer crosshatch vectors from the second Slice(all other vector types are removed including near-flat down-facingcrosshatch). These hatch and fill vectors are still distinguished byblock headers that indicate which Merge object they came from. Thereforethe combined file can be built as a single object.

One must be sure to give the proper exposure values to each vector type.Therefore, the hatch vectors from the second slice object are givenassociated exposure values equivalent to skin fill. This procedure willproduce an object substantially like that described above. However,there are several differences between this implementation and thatdesired. First the regions of down-facing features and up-facingfeatures might be given a double exposure (and therefore extra undesiredcure depth) depending on whether the crosshatch from the second Slice ofthe object is still included in the combined file or not. Second, sincethe present Slice program doesn't generally separate non-down facinghatch from down-facing hatch (except in the near-flat regions), therewill be an additional cure in the down-facing regions since thecrosshatch must be overcured somewhat to insure adhesion betweencross-sections.

FIGS. 14a and 14b depict a side view of an object built according to thetechniques of this first embodiment. FIG. 14a represents a side view ofthe CAD designed object. The dotted regions indicate solid regions. FIG.14b represents a side view of the object as built according this firstpreferred embodiment wherein every third layer is skinned to helpincrease the structural integrity of the object. The regions labeledwith forward slashes, "/", indicated regions that are skinned becausethey are down-facing. The regions labeled with back slashes, "\",indicate regions that are skinned because they are up-facing. Theregions that are labeled with X's indicate regions that are to beskinned according to the teaching of the present embodiment that wouldnot otherwise be skinned. Layers 1, 4, 7, and 10 are to be skinnedaccording to this embodiment.

In a second preferred embodiment an object is built by providing andexposing boundary vectors on each layer, crosshatch on each layer andskin fill vectors on each portion of each layer. As with the previousembodiment and the following embodiments, this second embodiment is notrestricted to part building with the use of vector data. The vector datais simply used as an implementation of the concepts of the invention andother methods of implementation could be used. Certain concepts of theinvention deal with amount of solidification on each cross-sectionand/or the order of material solidification on each cross-section and/orthe depth of solidification of each region on each cross-section. Thissecond embodiment is similar to the first described embodiment exceptthat now skin-fill is supplied on every region of every cross-sectionnot just with down-facing features, up-facing features, and withperiodic cross-sections. This second embodiment therefore results ingreen parts that have little or no substantially untransformed materialtrapped internal to their boundaries. There will be no substantiallyuntransformed material if the effective skin depth thickness is equal toor greater than the layer thickness. There will be, to a greater orlesser extent, some substantially untransformed material if theeffective skin cure depth is less than the layer thickness. As with theprevious embodiment, it is desired to get some net overcure betweenregions of a cross-section that overlap with regions of the previouscross-section to insure adequate adhesion, but it is desired indown-facing regions that the net cure depth be uniform and be of only aone layer thickness depth. It has been found that with embodiments likethe present one, where substantially all material on each cross-sectionis substantially transformed, that vertical curl can and generally doesgo up significantly but that horizontal distortion goes downsignificantly. It is known that the amount of curl (both horizontal andvertical) can vary tremendously depending on the amount of overcurebetween layers; the amount of overcure between adjacent lines on thesame cross-section; the extent of the area over which the overcure takesplace; the thickness of the layers; and the order ofintercross-sectional solidification as well as the order ofintracross-sectional solidification. If parts are to be built thatcontain few unsupported critical features, or in which the unsupportedfeatures can be supported by Webs, the direct application of thisembodiment can lead to substantial improvements in part accuracy.

If the part to be built does contain critical regions that cannot bewell supported then modifications to this embodiment can be helpful inreducing the vertical "curl" type distortion that may result. Thesemodifications might include the use of the techniques of this embodiment(or "continuous skinning" or "skintinuous") on only the regions that areor can be adequately supported and continuing to use the standardbuilding methods of boundaries, widely spaced crosshatch, down-facingfeature skinning routines, and up-facing feature skinning routines onthe other regions of the part. "Strongarm" building techniques can beeffectively used in these other regions of the part. The result of thismodified approach would be substantially increased horizontal accuracyin the supported regions with no sacrifice in vertical accuracy in theunsupported regions.

Other modifications, to avoid increased vertical distortion include theuse of Smalleys, described in U.S. Pat. No. 5,015,424; the use ofMultipass drawing techniques, described in U.S. patent application Ser.No. 182,823, now abandoned, and U.S. Pat. No. 5,104,592; the use ofRivet type layer to layer adhesion techniques, described in U.S. patentapplication Ser. No. 182,823, now abandoned, and U.S. Pat. No.5,104,592; the use of "strongarm", "log jam", and "quilting"; as well asother techniques to be described hereinafter; and similar techniques;and combinations thereof.

As with the previously described first embodiment method of building,this method of building can be substantially implemented by Slicing thedesired CAD object file, or the like, twice and then Merging the filestogether. The first Slice is done with relatively normal Slicingparameters, except no skin fill is used. One example is by using X and60/120 crosshatch with a 50 mil spacing. The second Slice is done,again, without the use of skin fill but with the use of closely spacedcrosshatch of type and spacing equivalent to that which is desired forforming skin fill on each layer. For example the second Slice may bedone with the same layer thickness but with only X type crosshatchspaced at 3 mil. After creation of the second Slice file, the two filesare Merged together using Merging options that keep all the vectors fromthe first Slice (except any skin fill vectors that were used) and thatkeep only the X crosshatch (including near-flat down-facingcross-hatch)from the second Slice file (all other vector types areremoved). The hatch from the first Slice and the fill vectors from thesecond Slice (actually hatch vectors the second Slice) are stilldistinguished by block headers that indicate which Merge object they arefrom. Therefore the combined file can be built as a single object beingsure to give the proper exposure values to each vector type. Thereforethe hatch vectors from the second slice object are given associatedexposure values equivalent to skin fill. This procedure will produce anobject substantially like that described above as the preferred methodof this embodiment. However, there is a difference between thisimplementation and the desired one described above. Since the presentSlice program doesn't generally separate non-down facing hatch fromdown-facing hatch (except in the near-flat regions), there will probablybe an additional cure in the down-facing regions since the crosshatchmay need to be somewhat overcured to insure adhesion betweencross-sections.

With the second embodiment and the first embodiment as well as withembodiments described hereinafter, there are many ways to use theexisting commercial software or to modify the outputs from the presentcommercial software to at least partially implement the variousembodiments. The implementations herein are only meant to be examples ofsuch techniques.

In a third preferred embodiment each cross-section is supplied withboundaries and skin fill vectors only (this embodiment does not utilizecrosshatch). In this third embodiment the boundaries may be cured to aneffective depth equal to the layer thickness or greater than the layerthickness depending on whether they are to be used to obtain adhesionwith the previous cross-section or whether they are to be used to form adown-facing feature. As with the previous embodiment the skin vectors innon-down-facing regions may be cured to a depth less than, equal to, orgreater than the layer thickness. It has been found that if skin vectorsare cured to an effective depth greater than the layer thickness, byusual curing techniques, vertical curl will be greater. Therefore, if itis desired to cure the skin vectors to such a depth it is advisable toutilize a drawing method that will help to reduce curl, such asmultipass. Multipass is a method of solidifying material in at least atwo step process, wherein a first exposure of material to thesynergistic stimulation leads to a depth of cure less than the layerthickness and the second pass (or higher order pass) results in a netcure depth that insures adhesion. Multipass is an effective way ofreducing curl. An additional enhancement of multipass scanning isdescribed in U.S. Pat. No. 5,182,056 regarding the use of multiplewavelengths during the multiscanning process. A short penetration depthexposure is given on the first one or more passes to insure thatsubstantial transformation of building material occurs prior to one ormore additional exposures using long penetration depths that are used toobtain and insure adequate adhesion between cross-sections.

An additional problem that might occur with this third embodiment isthat of excessive horizontal curl. In the previous embodimentshorizontal curl was kept to a minimum by the exposing of cross-hatchprior to the exposing of skin, wherein the cross-hatch would act as astabilizing frame upon which skin could be formed. Since this thirdembodiment doesn't contain cross-hatch it may be necessary to utilize ahorizontal curl reduction technique also.

Such techniques include the use of nonconsecutive vector drawing, theuse of non-overlapping fill vectors (e.g. "weave" which is the topic ofembodiments to be described later), and the filling of non-consecutivelydrawn vectors by intermediate vectors (in many respects this is ahorizontal version of the multipass technique described above). Thenon-consecutive ordering of vectors refers to a technique of supplyingfill or hatch vectors with a particular spacing and then exposing thevectors in a nonconsecutive manner. In traditional stereolithographyfill vectors are cured in a consecutive order.

An example illustrating the differences between consecutive ordering andnon-consecutive ordering is depicted in FIG. 7. FIG. 7a illustrates across-section of boundary 200 and containing unidirectional fill vectors201 to 209. In traditional stereolithography the order of drawing isfrom vector 201 to vector 209. The direction of scanning each of thesevectors has generally been such that the amount of jumping betweenvectors is minimized. The odd numbered vectors have generally been drawnfrom left to right and the even numbered vectors have been drawn fromright to left. Therefore the entire fill can be drawn with minimaljumping between the head of one vector and the tail of the next.

FIG. 7b illustrates a similar cross-section but wherein an example ofnonconsecutive drawing order is used to minimize any horizontal curlthat might have a tendency to occur. The cross-section is surrounded byboundary 220 and it is filled with vectors 221 to 229. The drawing orderis from 221 to 229, therefore every other vector is skipped on a firstpass of drawing and then the vectors skipped on the first pass arescanned on a second pass. This technique is especially useful forminimizing curl when two consecutively scanned vectors are separated bya distance so that the material cured by each vector individuallydoesn't connect to the material cured by the consecutively scannedvectors. Then on a second pass (or later pass) the gaps between thematerial exposed by the first pass are filled in by the additional passwhich scans vectors intermediate to those of the first pass. If thewidth of cure of each vector is relatively wide compared to spacingbetween vectors it may be necessary to skip more than just every othervector. For example it may be necessary on a first pass to cure onevector and skip three vectors then cure another vector and skip the nextthree vectors, and so forth. On the second pass one may then cure theintermediate vector of each set of 3 vectors not drawn on the firstpass, and then finally on a third pass the remaining unexposed vectorsare scanned. This is illustrated in FIG. 7c. The boundary 240 is filledwith vectors 241 to 249 wherein the scanning order is 241 to 249.

If the skin vectors will only be given an effective cure depth less thanor equal to the layer thickness it will likely be necessary to supplyadditional exposure in the form of point rivets, or the like, on theportion of the present cross-section that overlaps the previouscross-section. The proper use of rivets will lead to adequate adhesionbetween layers but will also tend to keep vertical curl to a minimum. Aswith the deeper cure depth methods this approach may also require theuse of horizontal curl reduction techniques.

As with the previously described methods of building, this method ofbuilding can be substantially implemented by a user by Slicing thedesired CAD object file, or the like, a single time. The part is slicedwith cross-hatch but without skin vectors. The crosshatch vectors arespaced with a separation typical for skin fill. One or more crosshatchtypes may be simultaneously used. For example, one can use both X and Yhatch with a spacing of four mils each. If the maximum cure width ofcure for a single pass along one vector is equal to or greater than thespacing between vectors (e.g. 12 mil MCW) and one doesn't wantconsecutively cured vectors to effect one another then a drawing patternsimilar to that described for FIG. 7c can be used for each type ofcrosshatch. This procedure will produce an object substantially likethat which would be produced by the preferred methods of the thirdembodiment. However, there is a difference between this implementationand the desired one described above. Since the present Slice programdoesn't generally separate non-down facing hatch and boundaries fromdown-facing hatch (except in the near-flat regions) and boundaries,there will probably be an additional cure in the down-facing regionssince the crosshatch may be somewhat overcured to insure adhesionbetween cross-sections.

A fourth embodiment is similar to the third just described but itdoesn't use boundary vectors either. Therefore, this embodiment suppliesand exposes only fill type vectors. Since there are no boundariesassociated with each cross-section in this embodiment, and thereforenothing other than surface tension and viscosity to hold the vectors inplace as they are drawn except where there is horizontal contact toadjacent vectors and vertical contact with the previous cross-section,the vectors of this embodiment must be drawn in a highly ordered manner.The vectors must be drawn in an order and/or to a depth that assuresadequate structural support to insure that each vector stays in placeuntil the entire cross-section is drawn. If the vectors are drawn in animproper order, then it is possible that some of them will drift out ofposition or be distorted out of position prior to the completion of theexposure and solidification of the cross-section. Since vertical curlgenerally occurs between material cured on the presently drawncross-section and material cured on the previously drawn cross-section,vectors in this region can be drawn in a nonconsecutive order and canalso be cured using two pass multipass to insure minimal curl.Subsequently, the vectors that occur in down-facing regions can be curedin a non-consecutive interlaced manner with vectors from the other hatchtypes. For example, one or more nonconsecutive X type vectors can bescanned followed by the scanning of one or more Y type vectors and thenrepeating the exposure of other X type and Y type vectors until all thevectors have been scanned. In this region the direction of scanning canbe just as important as the order of scanning. To insure the mostappropriate positioning of vectors they may need to be scanned from thesupported region towards the unsupported region.

Other embodiments, described hereinnext, create at least a substantialamount of fill on a cross-section in a manner more analogous to standardapproach crosshatch vectors. That is by supplying and exposing vectorswhich are spaced such that they do not effect each other during theirexposure. They are spaced at or slightly above the expected maximum curewidth of the individually exposed vectors. Thereby, after exposure ofall vectors a substantially transformed cross-section results with onlyminimal untransformed material between the vectors. The variousembodiments of this approach are broadly known by the name "Weave".

The name "Weave" particularly applies to the first preferred embodimentof this concept (the fifth embodiment of this application). Thisembodiment is the presently most preferred embodiment of the variousSkintinuous building techniques. This embodiment consists of supplyingand exposing boundary vectors, next supplying and exposing at least twotypes of non-parallel cross-hatch, wherein the exposure of the firstcross-hatch type is insufficient to produce a cure depth that results inenough adhesion to induce vertical curl to the previous cross-sectionand wherein the exposure of the second cross-hatch type is equivalent tothe first type, thereby resulting in sufficient exposure in theoverlapping regions to cause adhesion between cross-sections. Thespacing of the crosshatch vectors is such that they are spaced slightlyfurther apart than the maximum cure width of the individual vectors whengiven the appropriate exposure to result in the desired cure depth.

As with the previously described methods of building, this method ofbuilding can be substantially implemented by using SLA software to Slicethe desired CAD object file, or the like, a single time. The part isSliced with cross-hatch but without skin vectors. The crosshatch vectorsare spaced with a separation slightly greater (e.g. 10%) than theexpected maximum cure width. The presently preferred system for buildingparts using this embodiment is the SLA-250 manufactured by 3D Systems,Inc. of Valencia Calif. The presently preferred building material is XB5081 stereolithographic resin (liquid photo-polymer) manufactured byCiba-Geigy. The presently preferred system utilizes a HeCd laseroperating at 325 nm which typically results in a width of cure ofapproximately 10-11 mils or less for a cure depth of 8-9 mils.Therefore, the crosshatch vectors are spaced at approximately 12 mils.The presently preferred fill vectors are combined X and Y crosshatch.The presently preferred SLA software is version 3.60. When using thepresently preferred software, an object is built by exposing boundaryand hatch vectors. As stated earlier, adhesion between cross-sections isobtained at the intersection points between the two hatch types. Thecure depth of these intersection points is approximately 12 to 14 milswhen parts are built with 10 mil layers. This method of building resultsin substantially less horizontal distortion and equivalent or lessvertical distortion than when equivalent parts are built with standardtechniques. Measured post cure distortion is substantially less than forparts built using conventional methods.

The formation of a cross-section by this fifth embodiment is depicted inFIG. 8a to 8i. FIG. 8 represents a square cross-section which is to becured to a uniform depth. FIG. 8a depicts a top view of the materialcured by scanning of the boundary vectors. FIG. 8b depicts a sectionalview of the material cured in FIG. 8a along line b. The cure depth ofthe boundary vectors is the layer thickness plus some overcure amount(e.g. 10 mil layer thickness +6 mil overcure). FIG. 8c depicts a topview of the material cured in response to the scanning of the Xcross-hatch on a dashed background of material cured in response toboundary vectors. FIG. 8d depicts a sectional view of the material curedin FIG. 8c along line d--d. The cure depth of the X crosshatch is lessthan one layer thickness (e.g. 8 mil cure depth for a 10 mil layerthickness). The exposed regions are relatively wide compared to theunexposed regions. That is, the spacing between hatch vectors was onlyslightly more than the maximum cure width of the hatch vectors (e.g. 12mil spacing of hatch vectors and an 11 mil maximum cure width).

FIGS. 8e and 8f show similar cured material for Y crosshatch vectors.FIG. 8g depicts a top view of the superposition of material cured asdepicted in FIGS. 8a, 8c, and 8e. The small square zones in the FIGURErepresent uncured material. The size of these squares is about 11 mil onedge or less whereas the solidified material between them is about 11mils on edge. FIG. 8h represents a side view of the cured shape ofmaterial along the line h--h of FIG. 8g. Line h--h is directly above themaximum cure from an X hatch vector. FIG. 8i represents a side view ofthe cured shape of material along line i--i of FIG. 8g. The cure depthof the regions where the X and Y hatch vectors overlap has increased tosomething greater than the layer thickness. Line i--i is located betweenthe cure of two adjacent X hatch vectors. Most of the area of thecross-section is more like FIG. 8h than FIG. 8i. The exposure in FIG. 8hisn't uniform but the nonuniformity is less than that produced in thetraditional approach to skinning a surface during part building. Themain reason for this reduction is that there isn't a superposition ofdiscrete hatch vectors with a six mil over cure each which results in upto an 11 mil overcure, or more, at their intersection points combinedwith skin vectors that form a uniform layer thickness cure depth.Instead there is simply a double exposure of closely spaced hatch thatproduces a substantially uniform cure depth with points of approximately5 mil overcure superimposed on it.

A variation of this fifth embodiment is to use weave in allnon-down-facing regions and to use other more traditional approaches toskinning (including the uniform skinning methods described below) on thedown facing features and to give these down-facing features a layerthickness cure depth.

A sixth embodiment of the present invention is similar to the fifthembodiment just described except in the sixth embodiment the crosshatch(or fill vectors) are offset or "staggered" from layer to layer. Oneimplementation of this method is to offset the vectors on adjacentlayers by 1/2 the hatch spacing. Therefore, the hatch vectors on everyother layer overlay the same hatch paths. Other forms of layer to layeroffset are possible wherein the overlaying of hatch paths (hatch pathsare lines on a given cross-section that have the potential of beingcrosshatched) is repeated at some other period than on every otherlayer. For example hatch paths may not overlay each other for 3 or morelayers.

Offset or "staggered" crosshatch may be utilized with standard buildingtechniques as well as with the various embodiments of the presentinvention. The advantages of using offset crosshatch with standardbuilding techniques (that is widely spaced hatch) involve the productionof smoother vertical surfaces of an object, more uniform volumetricproperties, and possibly less curl between layers since adhesion betweenlayers is due to points instead of lines.

In building parts for investment casting, hollow parts lead to lessstructural strain on the casting molds as the building material isburned away. Hollow parts can be built with crosshatch but withoutskins, thereby tending to allow untransformed material between thecross-hatches to drain from the object. Solid parts tend to expand andcrack investment casting molds, whereas hollow parts have less of atendency to do so. However, building hollow parts can be a problem evenwhen skin fill isn't used if the hatch vectors on successivecross-sections lie on top of each other. Untransformed building materialcan be trapped between the cross-hatch and the boundaries. The trappedmaterial can later become solidified, thereby losing the desired hollowpart characteristics of the object. However, if thecentering-to-centering distance between crosshatch vectors is greaterthan approximately twice the maximum cure width, then offsetting thevectors by 1/2 the spacing on every other layer will result in a partwhere substantially all of the internally untransformed material canflow through various gaps and thus can be removed prior to using thepart to make an investment casting mold. This advantage of offsetcrosshatch is illustrated in FIGS. 9a and 9b.

FIGS. 9a and 9b illustrate the sixth embodiment and depict side views ofan object whose boundary vectors are offset from one another but are notoffset sufficiently to allow drainage of untransformed material betweenthem (these are nonvertical but steep boundaries as opposed to flat ornear-flat boundaries). FIG. 9a depicts a part built with overlayingcrosshatch and therefore pockets of untransformed material trappedwithin it. FIG. 9b depicts the part built with offset crosshatchtherefore allowing pathways for removal of internal untransformedmaterial. Assuming the top of each partially depicted object reconvergesso that building material cannot be removed from the top, as shown inFIG. 9a, only pockets 306 and 308 can drain whereas 302, 304, 310, and312 cannot drain. In FIG. 9b, the entire internal area of the part formsone interconnected pocket from which substantially all untransformedmaterial can drain. If using a photopolymer, drainage can be enhanced byutilizing elevated temperatures to reduce resin viscosity. Since aprimary principle of the present invention is to solidify as muchinternal material as possible this sixth embodiment of offset crosshatchdiverges from the skintinuous building techniques. But it is a usefulbuilding method in its own right. Its ability to reduce post curedistortion is discussed in Example 6.

The above building technique, which produces drainable parts for use asinvestment casting patterns, has become known as a QUICKCAST BuildStyle. This is a generic name that can be applied to any of a variety ofstereolithographic build styles that can be used in forming objects withhollow or drainable walls.

Presently preferred QUICKCAST building techniques use widely spacedcross-hatch vectors that are derived from hatch paths that are fixed fora number of layers. This causes the hatch lines that are produced fromthe hatch vectors to overlay each other for a number of layers. Afterforming several layers, the hatch paths are shifted and remain in thisaltered state for a number of layers after which they are shifted backto their original locations. In effect, the shifting of hatch lines onlyoccurs periodically. The most appropriate hatch spacing and hatch heightbefore shifting are resin dependent. It has also been found that theseparameters can also be dependent on object configuration. When castingthe stereolithographically formed patterns, it has been found that ifthe thickness of completely solid material exceeds 80 to 120 mils theceramic mold shells may crack when attempting to burnout thestereolithography pattern. Thus, when forming objects it must be ensuredthat regions thicker than 80 to 120 mils do not contain trapped resinthat could become solidified upon post cure irradiation. This in effectpresents an upper limit on how many consecutive layers can containoverlapping hatch if the pattern is to be used for arbitrary objectconfiguration. If the layers of overlapping hatch approach the 80 millevel, it is apparent that an arbitrary object configuration mightcontain regions which could become prohibited from draining. On theother hand, if the layers of overlapping hatch become too thin, thevertical openings between the offset hatch lines may become too small toallow effective drainage of the liquid resin due to surface tension orviscous flow effects. Balancing the problems involved in setting theoverall hatch height, for typical object configuration the preferredthickness of layers before offset is in the range of 70 to 130 mils andmore specifically between 80 to 120 mils, and most preferably about 100mils plus or minus 5 mils and maybe 10 mils. For a given objectconfiguration, it may be advantageous to reduce the height before offsetto as low as 30 or 40 mils. However when lowering the height beforeoffset, one must expect significant increases in drainage time. It isnoted that when curing hatch vectors, they are typically supplied anexposure in excess of the layer thickness to ensure that the layersadhere to one another. This excess cure depth is typically 5 to 6 milsor more. This excess cure depth results in a decreased verticaldimension of the openings formed by the offsetting of hatch. Thisdecrease in opening height must be considered when determining thenumber of layers to draw before offsetting. The horizontal spacing ofthe hatch vectors is also bounded by opposing requirements. If the hatchspacing is made too small, the surface tension and/or viscous flowcharacteristics of the liquid might make drainage impractical, if notimpossible. On the other hand if the spacing of the hatch vectors is toowide, several problems could occur: (1) they might supply inadequatesupport for the skin and boundary regions surfacing the object, (2) theymight provide inadequate strength for overall object integrity, or (3)they might create trapped volumes that could make recoating difficult.For typical object configurations, it has been found that a spacing ofapproximately 120 to 180 mils is preferred; more specifically a spacingof 130 to 170 mils is preferred; and most preferably a spacing ofapproximately 150 mils is used. However, spacing of 100 to 250 mils havealso been found to be satisfactory. The presently preferred buildingmaterials for stereolithographically forming investment casting patternsare hybrid epoxy resins, SL 5170 and SL 5180. These resins aremanufactured by Ciba Geigy of Basel Switzerland and sold by 3D Systems,Inc. of Valencia, Calif. The SL 5170 is use in combination with a HeCdlaser emitting 325 nm radiation, while SL 5180 is used in combinationwith an argon-ion laser emitting 351 nm radiation or a krypton laseremitting 351 and 356 nm radiation. The preferred layer thickness for SL5170 is 4 mils with a boundary vector overcure of 7 mils, and otherexposure parameters including a hatch vector overcure of 5 mils incombination with a triangular hatch pattern, a skin vector spacing of 4mils and a net skin cure depth of 12 mils. The preferred layer thicknessfor the SL 5180 resin is 6 mils with a triangular pattern and otherexposure parameters including a boundary overcure of 7 mils, a hatchovercure of 6 mils, and with other parameters similar to those used forthe SL 5170 resin.

Though it is possible to heat the part to an elevated temperature tolower the resin viscosity to expedite drainage, it has been found thatthe most preferred temperatures are equivalent to the temperatures usedin forming the objects on the SLA. This temperature range is typically28 to 30 degrees C. If the temperature is increased significantly abovethis level, increase in object distortion due to temperature has beenfound to outweigh any advantage gained by decreased drainage time.

Though the above described version of the QUICKCAST build style workswell for making useable investment casting patterns, it has severaldrawbacks. These drawbacks include: (1) holes can be formed in the skinsand surfaces of the object due to support removal and/or due toinadequate adhesion between boundaries possibly due to a dewettingphenomena between the solidified resin and the liquid resin when verythin layers are used in forming the object, (2) as noted above, internalcavities can be closed off so as to trap resin, (3) insufficientdrainage from portions of the objects, (4) inadequate surface finish,(5) possible formation of trapped volumes, and (6) surface dimples.Based on these problems a new version of the QUICKCAST build style hasbeen developed. This new version adds one or a combination of newfeatures. These new features may include: (1) formation of multipledown-facing skins so as to increase the structural integrity ofdown-facing features, (2) no utilization of hatch vectors when formingat least the first layer of down-facing skin which minimizes anywafflish appearance of these features, (3) formation of multipleup-facing skins to increase the structural integrity of the up-facingfeatures, (4) no utilization of hatch vectors when forming at least thelast layer of up-facing skin thereby minimizing any wafflish appearancethat might result, (5) utilization of multiple boundaries which areoffset from one another when forming the exterior portions of eachcross-section thereby increasing the structural integrity of the wallsof the object, (6) exposing the most exterior boundary last on eachcross-section, (7) utilization of wider spaced hatch vectors thanpossible with the previous version, thereby decreasing drainage time anddecreasing the likelihood of trapping pockets of resin in tight regions,(8) utilization of different hatching styles than those preferred forthe previous version, eg., rectangular or hexagonal patterns, (9)automatic creation of holes in selected surfaces of the object so as toeliminate or reduce the formation of trapped volumes and so as to allowautomatic drainage of liquid from the object upon completion of objectformation and lifting of the object from the vat of resin; (10)compensation for use of down-facing skins with a thickness greater thanthe layer thickness. In the most preferred embodiment all of theseelements would be combined; however, it is conceivable that only aportion of these elements might be implemented in a particularembodiment wherein most if not all of the benefit of the preferredembodiment would be achieved for a given object configuration. In thecurrently preferred embodiment, the most preferred parameters when usingSL 5170 are: (1) use of 6 mil layers; (2) use of 4 boundaries spacedapart by 4 mils per consecutive boundary; (3) use of 3 up-facing and 3down-facing skins exposed using both X- and Y-fill vectors with each setof fill vectors supplied with sufficient exposure to yield an 8 mil curedepth with no hatch on the first down-facing layer or the last up-facinglayer; (4) use of a hatch spacing of between 150 and 350 mils and morepreferably between 200 and 300 mils and most preferrably approximately250 mils; (5) use of a square hatch pattern, though eventually ahexagonal pattern might be better; (6) though not yet automated, atleast one hole of an approximately 1/4-inch diameter at or near the topof the object, to act as a vent, and one, two or more holes ofapproximately 1/4-inch diameter each at or near the bottom of the objectto act as drainage zones. The values specified for these parameters canbe varied, for example, depending on the actual layer thickness to beused in forming an object, two skins may be sufficient or more than 3may be desired. In particular, implementation techniques for forming themultiple skins and boundaries can be found in U.S. patent applicationSer. No. 08/428,951, in combination with the teachings of U.S. Pat. No.5,321,622. The concurrently filed application is a continuation-in-partof U.S. patent application Ser. No. 08/233,027, filed Apr. 25, 1994, nowpending, which is a continuation-in-part of U.S. patent application Ser.No. 08/016,202, filed Feb. 9, 1993, now abandoned. Each of these patentsand applications is incorporated by reference herein as if set forth infull.

An additional embodiment of the QUICKCAST build style exists thatdoesn't necessarily use offset hatch to ensure drainability of theobjects being formed. Instead, in this embodiment the hatch vectors arenot drawn as continuous lines but are periodically provided with gapsthat are sufficiently large in both the horizontal and verticaldimensions so as to allow flow of the liquid resin and its eventualdrainage from the interior portions of the walls of the object. As withthe previous embodiments the spacing of the hatch vectors is preferablyequal to or greater than 150 mils. It was noted above with regard to theprevious embodiments, that if thin, vertical-features were in existenceon a given object then depending on the exact vertical dimensions of thefeatures, the exact vertical location of the features, and the verticallocations at which the hatch vectors are being offset; it is possiblethat liquid resin could get trapped between external boundaries,external skins, and the hatch lines. This is especially a problem withthe multiple skin embodiment since the use of these extra skinsdecreases the vertical dimensions of the open regions of these features,thereby increasing both the likelihood of trapping liquid and of havingthe overall solidified region exceeding the acceptable thickness. On theother hand these previous embodiments have little likelihood ofabsolutely trapping liquid in small horizontal features as long as thevertical dimensions of these features were not also small. In thepreviously described offset hatch embodiments, without implementing anobject feature sensitive embodiment, it is difficult to reduce theprobability of encountering these vertical traps. However, in theinstant broken hatch embodiment it is possible to reduce the probabilityof forming these vertical traps at the cost of increasing theprobability of encountering horizontal traps. However, if donecarefully, with this embodiment, both the vertical and horizontaltrapping situations can be maintained within levels that are not likelyto cause the overall solidified thickness to exceed the acceptablelevel. If an object has only small horizontal features as opposed tovertical features, one of the previous embodiments is probably wellsuited for building the object. If the object has both small verticalfeatures and small horizontal features the first example implementationof this embodiment is well suited for forming the object. However, ifthe object has only small vertical features, then the second exampleimplementation of this embodiment is well suited for forming the objectsince it leads to higher structural integrity but still allows liquid tobe readily drained from the object.

As a first example implementation of a broken hatch embodiment,reference is made to FIG. 26a, 26b, 26c, and 26d. FIG. 26a depicts theboundary 1002 for an arbitrary layer and the hatch pattern 1004 to becured in association with that layer. As can be seen the hatch lines tobe cured on this layer lie on a square grid of hatch paths 1006 (i.e.,the dash lines) but only the regions near the intersections of the pathsare actually solidified. If the spacing between the consecutive hatchpaths is, for example, 150 mils, the length of the individual linessolidified on each path may be between 30 and 50 mils. This results inopen horizontal regions of 100 to 120 mils between each solidified lineon each path. FIG. 26b, on the other hand, depicts a hatch pattern 1008to be cured in association with other layers of the object. This hatchpattern is based on the same grid of hatch paths 1006 that the shorthatch pattern 1004 was based on. Thus it is ensured that the hatch lineslie atop one another. In this embodiment the hatch patterns 1004 and1008 alternate on a periodic basis. This alternation of the patternsshould occur so that the object is formed with sufficient structuralintegrity. At the same time the alternations should be performed using aspacing such that the vertical dimensions of the openings aresufficiently large to allow efficient flow of the liquid material, whileat the same time not spaced so far apart so as to form structures thatwill trap liquid in features thinner than 80 to 120 mils. Based on thiscriteria, the 1004 hatch pattern is used on consecutive layers until aheight of 80 to 120 mils is obtained followed by use of the 1008 hatchpattern on the next consecutive layers for a height of 20 to 40 mils.This layer-to-layer build up process is depicted in the object side viewas shown in FIGS. 26c and 26d which are taken from vertical cuts througha plane of stacked hatch paths and a plane intermediate to the stackedhatch paths. As can be readily observed, this embodiment is lesssusceptible to trapping volumes of liquid that can result in solidifiedregions thicker than the acceptable level. Of course other hatchpatterns are possible which can lead to the same desired result. Theseother hatching patterns might be based on other hatch path patterns orspacings and/or other combinations of solid and broken hatch, or even ofbroken and broken hatch. For added structural strength, each hatch linemay actually be formed by exposing two or more slightly off-set hatchvectors.

Another embodiment may not allow the hatch lines on layers containingbroken hatch lines to contact the boundaries of the region. In fact aminimum separation distance can be implemented by creating a temporaryboundary for hatching purposes via a line width type of compensation ofthe original boundary.

The second embodiment is similar to the first embodiment above, exceptthat some of the broken hatch lines are allowed to extend further andthus provide more stability to the structure.

Additional QUICKCAST building style embodiments exist that can be usedin combination with the any of the above embodiments. Some of theseadditional embodiments involve the use of different hatching patterns atdifferent positions within the object depending on how far the positionsare from the surface of the object. When using a single skin and singleboundary offset hatch embodiment, the hatch must be relatively closelyspaced and offset frequently to ensure that the surfaces of the objectare adequately supported and that large regions of liquid won't betrapped within the object. However, closely spaced hatch and frequentlyoffset hatch implies that the flow paths are relatively small and thusconsiderable time may be required to complete the necessary drainage.Since the internal integrity of the object is less important than theexternal integrity, as one moves further from the surfaces of the objectthe spacing of the hatch vectors can be increased significantly. Thisincrease in spacing of the vectors, or other reduction in the quantityof hatch lines being used, can lead to decreases in drainage time sincethe resistance to resin flow is reduced. The first step in implementingan embodiment that changes hatch line quantity as one moves deeper intoan object, is to determine how deep one is into the object. Thetechniques for doing this are described in previously referenced, filedU.S. patent application Ser. No. 08/428,951, entitled "SimultaneousMultiple Layer Curing in Stereolithography." This referenced applicationteaches the use of layer comparisons to determine vertical depths intothe object and the use of erosion and expansion routines to determinehorizontal depth into the part. Using these techniques one can defineboundaries for each cross-section that are located at some predefinedminimum distance into the object from all surfaces and thus the curingof the material within these boundaries can be based on a modified setof criteria. In curing the regions within these boundaries theboundaries themselves need not be solidified, thus removing any concernsabout these deep boundaries limiting fluid flow. For example, if aparticular hatch spacing is preferred for use near the surfaces of theobject in order to support external boundaries and skins, that hatchspacing may be doubled in the deep regions of the object. For examplethe portions of the cross-section within 50-150 mils of the surface maybe given a hatch spacing of approximately 150 mils while portions deeperinto the cross-section may be given a hatch spacing of 300 mils. FIG. 27depicts a cross-section which uses two different hatch types dependingon the distance the region is from the surfaces of the cross-section.

In another embodiment, the use of the information about a region's depthinto the object can be utilized in an opposite manner to that of theprevious embodiment. Especially when using a multiple skin and multipleboundary embodiment, one can use less internal structure to support thesurfaces and external boundaries of the object. This use of less supportstructure can lead to much freer drainage of the untransformed materialwithin and near the external surfaces of the object. However, though thesurface areas are much more rigid one must still be concerned aboutoverall structural integrity of the object. Based on these concerns thisembodiment uses minimal internal structural near the surfaces andboundaries of the object and more structure when further from theexternal features of the object. For example, the hatch spacing may belarge when within a particular distance from the surface of the objectand/or it can be ensured that only broken hatch vectors are used withinthe given distance from the surface. One can then convert to closer ornon-broken hatch deeper into the interior of the object. Since it isonly the combination of boundaries and/or skin with hatch that cancreate trapped pockets of liquid (which can eventually become solidifiedand lead to failure during casting) and since this embodiment can beused to ensure that no trapped regions having dimensions that come closeto those which can result in a casting failure during burn out,embodiments based on these techniques are considered to be mostpreferred. Of course immediate embodiments exist that can focus only onhorizontal distance from boundaries or on only vertical distance. Thoughless preferred, these intermediate embodiments would probably producesatisfactory parts in many situations while simultaneously reducing thecomputational complexity of the embodiment.

As noted above, horizontal comparisons, as described in the SimultaneousMultiple Layer Curing Application, can be of particular advantage inimplementing advanced QUICKCAST build styles. The following is anexample of such as embodiment. In this embodiment, the horizontalcomparisons operate on the LB regions of each cross-section to dividethem into three regions. The first region is that closest to theoriginal LB boundaries and is approximately 15-30 mils wide. This firstregion forms a completely solidified shell region. The solidification ofthe first region may occur via multiple overlapping offset boundaries(preferred technique) or alternatively it may be filled by a utilizationof skin vectors. The second region borders the first region and proceedsdeeper into the cross-section another 50 to 100 mils. This region issolidified using minimal structure, e.g. a very wide spaced hatch, orpossibly a broken hatch pattern, that may be used on only periodiclayers. Each hatch line might be solidified via a single hatch vector orby two or more hatch vectors which are slightly offset from one another.For example, it/they might be used once every 25 to 150 mils and beoffset with consecutive uses. Alternatively, for example, it/they mightbe used every 100 to 150 mils but when used it/they may be exposed on aseries of two or three, or more, consecutive layers without offset. Thespacing between the lines might be 100 to 250 mils.

In this embodiment, the third region occupies the rest of the originalLB region. The third region is solidified with a tighter hatch pattern,or one with fewer breaks, than that used in the second region. Forexample, hatch with a spacing of 100 to 150 mils might be used on everylayer and offset periodically. This embodiment offers a strong outershell which is directly supported by a loose grid structure, which inturn is supported by a more rigid grid structure. As drainage ofstereolithographically produced investment casting patterns is criticalto their successful use, and as resin entrapment between the surfaces ofthe object and the hatch lines can result in failure of the ceramic moldon burn out, the utilization of the horizontal comparison techniqueallows implementation of an internal grid structure that is fine enoughnear the object surfaces to allow resin drainage but structurally rigidenough in the deep interior portions of the object to provide adequatesupport for large structures so as to ensure structural integrity.Without the horizontal comparison techniques described in the U.S.patent application Ser. No. 08/233,027, this embodiment could notreadily be implemented on an automated basis.

Furthermore, as noted previously, a more preferred embodiment willcombine the horizontal comparison generated regions with multiple skinsgenerated by vertical layer comparisons. This combination embodiment isreadily generated by the techniques described in the above referencedapplication.

The most preferred embodiment extends the last embodiment one stepfurther, by continuing the layer comparisons into one or more layersimmediately above the multiple down-facing skins and immediately belowthe multiple up-facing skins so as to provide region designations thatallow the regions immediately above and below the down-facing andup-facing surfaces, respectively, to be transformed using a minimalamount of hatch. Preferably, these regions extend beyond the skins by 25to 150 mils and most preferably by 70 to 100 mils and are solidifiedusing a series of point exposures, e.g. columns, which may be one, two,three or more line widths in diameter and spaced from each other by 25to 150 mils. Alternatively, the columns may not be circular incross-sectional dimension but may take on some other shape, such assmall crosses, boxes, or the like.

Other more advanced embodiments are possible where the most exteriorportions of the continuation boundary regions are not given a widenedsolid cure where the continuation boundary is bounded by a region whichis being skinned. In an extension of this embodiment, additional carecan be taken to ensure that object regions close to inside corners arenot inadvertently unexposed due to the potential lack of multiple skinsbeing copied into these corner regions and lack of widened continuationboundary zones.

Other embodiments of the nonoverlapping approach to building can bedeveloped from appropriate combinations with techniques discussed inconjunction with overlapping exposure techniques as well as with theadditional embodiments of the present invention to be describedhereinafter.

Besides the two main approaches described previously, that isoverlapping fill or non-overlapping fill on at least a portion of thecross-sections, there is an additional class of embodiments that areused to increase structural integrity. This next class of skintinuousembodiments are based on the curing of discrete points of materialcalled "Bullets" instead of the curing of overlapping or non-overlappinglines of material. The bullets are cured in association with a singlecross-section as a plurality of substantially nonoverlapping exposures.The embodiments of this approach comprise methods of solidifyingprimarily internal regions of objects whereas the down-facing andup-facing regions of the object may be cured by the other approachesdescribed herein.

The seventh embodiment of Skintinuous (the first embodiment of thisclass) involves curing the internal portions of desired cross-sectionsby exposing material within the boundaries of the cross-sections as aseries of discrete points. The points that are exposed on a givencross-section are spaced from each other by a distance slightly greaterthan the maximum diameter of the cured material formed upon exposure ofthe material to synergistic stimulation. In other words, on a singleinternal cross-section a substantial portion of the material is cured inthe form of point exposures with a small gap separating each pointexposure from its neighbors. This separation stops the transmission ofstress and therefore diminishes curl. Each point is cured to a depthequal to or slightly greater than the layer thickness to insure adhesionbetween cross-sections. On the next cross-section the pattern ofexposure is "staggered" or shifted so that the point exposures on thisnext cross-section are centered above the gaps between the points on theprevious cross-section. This shifting pattern of bullet exposures iscontinued on alternating cross-sections until the desired region of thepart is complete. This allows substantial structural integrity to bedeveloped between cross-sections while decreasing the amount of curlwhen building with a given layer thickness.

Two consecutive overlapping sample cross-sections are shown in FIGS. 10aand 10b. These sample cross-sections depict a cross-section boundary 400enclosing a series of point exposures. FIG. 10a depicts point exposures402 located on a particular grid while FIG. 10b depicts point exposuresoffset (staggered) from those in FIG. 10a. A comparison of the twoFIGURES indicates that the bullets on one cross-section are centered inthe middle of the space between bullets on the previous cross-section.FIG. 10c depicts substantially a side view of the combined FIGS. 10aalong line 10c--10c and 10b along line 10c'--10c'. This FIGURE, at leastin a 2 dimensional view, illustrates how the bullets are staggered fromlayer to layer. The illustrations of FIG. 10a and 10b depict aparticular arrangement of points on a given cross-section but otherarrangements are possible. For example to get a tighter fit of bullets(higher ratio of transformed to untransformed material on a givencross-section) one could locate the points in a hexagonal pattern. Thishexagonal pattern when combined with higher cross-sections could form ahexagonal close-pack structure. Therefore each bullet would have 6nearest neighbors on the cross-section as opposed to only 4 as shown inFIGS. 10a and 10b.

This method of building with bullets can only be partially implementedfrom present 3D Systems software. This implementation is only partiallysatisfactory. Proper utilization of this embodiment requires modifiedsoftware.

The implementation from the present software is done by slicing theobject with a single type of crosshatch vectors (e.g. X vectors) with aspacing slightly larger than the diameter of the bullets of materialthat will be formed. The object is sliced a second time with the partoffset by 1/2 the spacing along the direction perpendicular to thechosen crosshatch direction (e.g. the Y-axis). The two objects aremerged together using options that shift the second file by -1/2 thecrosshatch spacing along the perpendicular direction (e.g. Y-axis) and1/2 the crosshatch spacing along the X-axis. Also the merging optionsused remove all the vectors from the second slice file except for thecross-hatch vectors. Then the resulting file is edited to remove thehatch vectors from alternating slice files on alternating layers.

When vectors are cured using the present software they are not cured bya continuously sweeping beam but by a beam that jumps a small distance(e.g. integer multiples of 0.3 mils) known as the stepsize or SS, andthen it waits at each allowed SS position a period of time known as thestep period or SP (e.g. integer multiples of 10 microseconds). Theparticular positioning for both timing and jumping is based on thebeginning point of each vector that is drawn. When the object is built,the SS value used is equivalent to the spacing between vectors (e.g. 12mils or approximately an SS value of 40). Since the two files wereoffset when they were sliced along the direction perpendicular to thehatch direction and then shifted back together during merge, the Y-valueassociated with each bullet will be offset by 1/2 the crosshatch spacingon alternating layers. Since the files were merged then offset from eachother by 1/2 the cross-hatch spacing along the direction of thecrosshatch, the X-value associated with each component will be offset by1/2 the crosshatch spacing between alternating layers. This method ofimplementation is useable but not always satisfactory since in some ofthe extreme values, the X-component of each vector fall slightly (1/2the crosshatch spacing) outside the boundary of the cross-section. Othersoftware based methods of implementation using the present software arebased on slicing the part twice as described above but here each part issliced with a layer thickness twice as large as desired and one of theparts is shifted by 1/2 the layer thickness prior to slicing and thenshifted back during merging.

A useful tool for implementing this embodiment from the present softwarewithout a major change would be to include a parameter that would allowcrosshatch vectors to be reduced in length at each end by a specifiedamount. This would allow shifting along the direction perpendicular tothe hatching direction, along with the reduction of the vectors createdby the second slice by 1/2 the crosshatch spacing, followed by thereregistration of the files during merging. Also of use would be anediting program that could read through the merged file and removeselected vector types from appropriate cross-sections.

If one is building an object with an orientation that is substantiallymore susceptible to curl than a perpendicular orientation, thisembodiment may be modified to that of an embodiment of offsetunidirectional crosshatch. Here the direction of offsetting would be thedirection most susceptible to curl and the direction of the vectorswould be the less susceptible direction.

The eighth embodiment of the present invention is similar to the seventhembodiment but the bullets are cured so as to solidify material inassociation with the previous cross-section as well as the presentcross-section. Therefore the cure depth of each bullet is typicallyequal to or somewhat larger than two layer thicknesses. Accordingly, inthis embodiment, it is important, when working with a particularcross-section, to know not only the internal regions of the presentcross-section but to also know the internal overlapping regions of theprevious cross-section. The spacing of the bullets is somewhere betweenwhat it was in the previous embodiment and the diameter of the bullet atone layer thickness below the present cross-section. The adhesionbetween layers is gained substantially by adhesion between the sides ofthe bullets on the present cross-section at a position one layerthickness below their upper surface and the sides of the bullets on theprevious cross-section at their upper surface. A side view of the bulletpositions on adjoining layers is depicted in FIG. 11. It is noted thatthe present embodiment is primarily for regions of the object two ormore layers from down facing features.

In still other embodiments, transformation of material that is locatedon one cross-section may occur from exposures given in association withcross-sections two or more layers higher up.

As discussed above, several new skinning techniques can advantageouslybe used in connection with this invention, based on non-consecutiveordering of skin vectors. Traditionally, skin vectors are orderedhead-to-tail, such that a first vector pass is made along a fill pathfrom one boundary to an opposing boundary, and a pass along the nextvector is then made, slightly offset (e.g., typically from 1 to 4 milsfrom the first), from the latter boundary back to the first. However, ithas been found, in accordance with some of the preferred embodiments ofthis invention, that distortion can be reduced by appropriate,non-consecutive scanning and therefore nonconsecutive formation order ofskin fill. Specifically, the offset between vectors can beadvantageously increased (e.g., doubled or tripled, or more), such thatthe successive skin vectors have less impact, or do not impact, uponadjacent lines of cured building material for a given series of passesacross the surface of the region of the part being formed. Additionally,in one or more successive series of passes, additional skin vectors canbe drawn between those that had been drawn in the earlier series ofpasses. These embodiments preferably have crosshatch vectors on eachlayer as well as skin vectors.

Yet another embodiment according to which distortion can be minimizedinvolves skinning in different directions for different layers. Forexample, in a part having x- and y-hatch on each layer, odd layers canbe skinned in the x-direction and even layers in the y-direction, orvice versa.

In still another embodiment, skin fill can be provided in both x- andy-directions on a given layer having x- and y-cross-hatch.

A preferred embodiment, when using the SL 5170 resin and the SL 5180resin is called the ACES building style. Only boundaries and X and Yskin fill are used on each portion of each cross-section. The sequenceof exposing the X and Y vectors is alternated from layer to layer. Thefirst set of skin vectors exposed are given an exposure that results ina net cure depth of slightly under one layer thickness. When the secondset of vectors expose the material, the increase in cure depth resultsin adhesion. Typically, identical exposures are applied to both sets ofskin vectors. However, it is possible to use a larger exposure on thesecond set than that used on the first set. The preferred layerthicknesses are 4 mils for SL 5170 and 6 mils for SL 5180. Though notpreferred it is possible to utilize hatch vectors during exposure of thecross-sections, furthermore it is possible to use the ACES buildingstyle on a portion of a cross-section or object and some other buildingstyle on another portion of the cross-section or object. The ACES buildstyle yields highly translucent parts.

When using epoxy resins like SL 5170 and SL 5180, it has been foundhelpful to allow a time period of between 5 and 90 seconds afterexposure of each cross-section before beginning the recoating process soas to allow the modulus of the exposed resin to increase to a certainminimum level before subjecting the newly exposed layer to the forcesinvolved in recoating. This time period is called the predip delay. Forthe ACES building style when using SL 5170 the time period is typicallybetween 10 and 30 seconds whereas when using SL 5180 it is typicallybetween 45 and 90 seconds. For, the QUICKCAST build styles when using SL5170, the predip delay is typically between 0 and 15 seconds whereaswhen using SL 5180, it is typically 10 to 30 seconds. Exact values ofpredip delay can be obtained from minimal trial and error for particularpart geometries.

As a technique for eliminating or at least minimizing the impact thatpredip delay has on part building time, it is possible to use a smartexposure pattern that exposes critical areas first, followed by exposureof less critical areas. In effect, the countdown of the predip delaytime can begin as soon as all critical regions have been exposed. Thusdepending on how long the exposure of the less critical regions takes,the predip delay is either eliminated or at least reduced. Criticalareas can be considered external boundary regions and external skinregions, with only a grid structure of the non-external regions beingconsidered at least marginally critical. One potential alternativeinvolves scanning external regions first followed by scanning a gridpattern in the non-external regions, after which the predip delaycountdown begins, followed by exposure of the remaining non-externalregions. The predip delay alternative with the ACES building style canbe implemented via non-consecutive skinning techniques wherein theboundaries are exposed, followed by the first skin exposure, followed bythe second skin exposure wherein critical regions are exposed first(which may be located in one or more distinct boundary regions) followedby a second, and possibly higher order, interlaced exposure.

According to a most preferred embodiment, however, x, 60° and 120°cross-hatch is provided with skin fill in at least one of the x, 60°, or120° directions, and preferably, in each of the directions. In apreferred variation of this embodiment, discussed in more detail below,the skin vectors of a given direction are not traced directly over thehatch vectors of the same direction, thereby avoiding excess exposure ofany given location. Moreover, since exposure is provided in threedirections over any given point in a skinned layer, the vector scanningspeed can be increased by a factor of three to yield one-third of anormal exposure per vector, resulting in a uniform exposure after allthree directional passes are made.

Another embodiment is that of "tiling". In this embodiment one of thepreviously mentioned approaches is utilized in exposing individual"tile-like" regions wherein small spacings of material between theindividual tiles are left untransformed to act as stress relief zones.The size of the individual tiles can range from that of a point exposureto that of an entire cross-section.

Tiling is a method of forming a layer of an object produced bystereolithography, wherein the layer is divided into a series of areaelements or tiles. Each area element is isolated from adjacent areaelements by spacings. The spacings around each area element remainuntransformed, at least until all neighboring area elements or tiles aretransformed or solidified. The spacings between the individual tiles areleft untransformed to act as stress relief zones. The width of thespacing is typically small compared to the width of the individualtiles. Individual tiles can be drawn with borders or without; however,it is presently preferred to draw tiles without individual borders.

Tiling can also be used as another technique of curl reduction whenimplemented on a second or higher layer above a down-facing feature.Generally no curl is generated on a down-facing feature so there is noneed for tiling as a curl reduction technique on a down-facing feature.It should also be noted that tiling does not generally apply todown-facing features because there is no underlying structure to attachindividual tiles to during the transformation process, i.e., tiling maybe applied only to an at least partially supported area as opposed to acompletely unsupported area.

Since the tiles are individual and discrete relatively small areas, theuse of tiles limits shrinkage to the boundary of the tile. This reducesstress and curl on the tiled layer, an especially importantconsideration in the first few layers immediately above a down-facingfeature. Curl generally occurs mainly in down-facing features. Thesefeatures curl upwardly as a result of the formation of the next severaloverlying layers. On the other hand, a potential disadvantage of tilingis that it possibly provides less strength.

The spacings between the tiles can be transformed or solidified(referred to as grouting or mortar) usually after all of the tiles havebeen formed. An entire object can be made by tiling to reduce posttreating. This grouting is usually transformed to a lesser degree thanthe tiles (a lower exposure is used).

By way of example, when using a presently preferred material such asXB5081 and 5 mil layers, tiling may be used in forming the first throughtwentieth layers above a first layer of a down-facing feature andespecially to form layers 1 through 10 (assuming the first layer issupported). If 10 mil layers are used, tiling would preferably beapplied in the range of the 1st through 10th layer and especially in the1st through 5th layer above a down-facing feature.

Preferably, the tile sizes range from the width of a laser beam (about0.010 inches, 1/4 mm) up to about 0.120-0.150 inch, with the mostpreferred range being from 3/4-2 millimeters on edge.

The spacings or gaps between the tiles should be as small as possible,within the limits of accuracy of placement and cure width of a beam ofsynergistic stimulation. The typical width of these gaps is in the rangeof 1-10 mils after exposure and cure. It is important that the materialin the spacings or gaps not be transformed or solidified sufficiently totransmit stress.

After forming one or more layers with tiling and without grout it isgenerally desirable to start offsetting tiles from layer to layer or tobeginning grouting between tiles or to stop the tiling processaltogether in order to insure adequate structural integrity of the part.As stated earlier, a potential problem with forming parts utilizingtiling is the tendency towards structurally weak parts. However iftiling is to be discontinued, grouted, or offset, it is important tominimize any tendency toward reintroducing curl that may result fromclosing the gaps. As the gaps are closed, any shrinkage of material thatoccurs above the gap, while the shrinking material is adhered to bothends of the gap, can cause curl distortion by tending to bring the topends of the gap closer together (closer than the spacing between thebottom edges of the gap). Since gaps result in relatively weak axes,this scenario of reintroducing curl is very likely. Additionally, it haslong been suspected and recently experimentally verified that shrinkageof curing material can still be occurring several seconds after exposureof an area is suspended. This means that closing a gap with a line ofcuring material which is adhered to the first side, and extended fromthe first side to the second side, and adhered to the second side withina few seconds can induce stresses into the part which can eventuallylead to distortion.

A preferred method of closing gaps, and thereby insuring adequatestructural integrity of a part, while avoiding reintroduction of curl,is based on insuring that at least a substantial portion of the materialcured over the gap is allowed to shrink prior to adhesion to both sidesof the gap.

A first embodiment of this method slightly offsets the tiles on a secondlayer from the corresponding positions of tiles on the previous (first)layer, wherein the offset is such that the tiles on the second layersubstantially cover the gaps between the tiles on the first layerwithout completely bridging the gaps, thereby avoiding the simultaneousadhesion of a single cured shrinking mass to both sides of the gaps onthe first layer. Thereafter, allowing for sufficient time for the tilesand the tile material spanning the gaps to complete their shrinking,grouting between the tiles on the second layer is formed. This groutingcompletes the bridging of the gap with only minimal shrinkage ofmaterial over the gap while adhesion to both sides exists. Since thisgrouting is offset from the gaps on the first layer, and since shrinkageof material on the second layer over the gaps occurs before the groutingis formed, substantially less curl is introduced. Any desired exposurecan be used in forming the grouting, without necessarily being limitedto grouting of lower exposure than that used to cure the tiles.

This first embodiment is depicted in FIGS. 23a to 23c. FIG. 23a depictsa side view of a portion of an object comprising a first layer which isformed with tiles and a second layer with slightly offset tiles andoffset grout. The tiles of the first layer are indicated with numeral800. The tiles of the second layer are offset sufficiently from tiles onthe first layer to substantially cover the gap area of the first layerwithout being offset so far as to adhere to the adjacent tiles on thefirst layer. These tiles of the second layer are depicted with numeral804. The grouting between the tiles on the second layer is cured afterthe tiles 804 on the second layer have been allowed to shrink (e.g.,generally at least a 3 to 5 second delay between completing neighboringtiles and beginning to grout). The grouting is indicated with numeral808. FIG. 23b depicts a top view of the tiles 800 of the first layer andFIG. 23c depicts a top view with superimposed tiles 800 of the firstlayer and tiles 804 of the second layer and the grouting 808 of thesecond layer.

A second embodiment of this method forms the second layer, on which thegaps will be closed by floating at least one end of the solidifiedmaterial which spans the gap until after at least a substantial portionof the shrinkage has occurred. After allowing for shrinkage to occur,the floating end(s) can be tacked down with rivets, or multipass, or thelike.

FIG. 24 depicts a side view of a gap 810 between tiles 800 on a firstlayer being closed off on a second layer by floating at least one end ofbridging material 814 until the bridging material has completedshrinking. The rivet completing the closure is depicted with numeral818.

Additional embodiments of this type involve the progressive partialclosure of the gaps over a plurality of layers. For example a gap can bepartially narrowed from one or both sides on a second layer followed byadditional narrowing or complete closure on the third or higher layer.

These methods of closing gaps between tiles are applicable to theclosure of the stress relief gaps disclosed in U.S. Pat. No. 5,015,424.As will be apparent to those of skill in the art these methods can bemodified or/and combined with themselves or other curl reductiontechniques to effectively close gaps without reintroduction ofsubstantial curl.

Where a scanning mirror-directed laser beam is used to transform thematerial, the "jumping" speed from tile to tile across the spacings mustbe considered. The mirror(s) directing the laser beam has a moment ofinertia which limits its rate of angular acceleration. If the laser isto jump from the edge of one tile to the adjacent edge of another tile,the jumping speed is limited since there is only a very small distancein which the mirror can accelerate before it must begin to decelerate toproperly direct the laser onto the edge of the next adjacent tile. Sincethe jumping speed is limited, the material in the gap may beinadvertently partially cured by the jumping laser beam. In tilingmethods wherein the laser is frequently jumping back and forth betweentiles, this can become especially problematic.

Inadvertent curing of the material in the gaps during jumping betweentiles can be overcome in several ways. The mirrors can be made toaccelerate faster, although a practical upper limit is quickly reached.Alternatively, a shutter can be provided to block the laser beam beforereaching the scanning mirror. However, mechanical shutters also sufferfrom inertial lag and are considered too slow to be effective.Electrically driven crystal acousto-optic shutters can be considered. Athird technique, i.e., the "long jump" technique is the most preferable.In the long jump technique, the laser beam jumps from a far edge of atile, accelerates over the tile (the launch tile), then crosses the gapat maximum velocity to a distant point on the adjacent tile (the landingtile), decelerates and begins to transform the area of the tile near itsfar edge. By making the long jump, the laser has a sufficient distancein which to accelerate such that it passes over the gap at a high speedand decelerates to the landing point distant from the gap.

Tiles can be formed in various patterns and shapes. One basic way is toform square or rectangular tiles in a straight grid pattern, i.e., withthe gaps or grout lines extending continuously in the two directions ofthe layer (x and y directions). However, with this grid pattern, thegrout lines themselves are relatively long lengths of material whichwhen cured are subject to curling. Moreover, the tiles forming thesimple grid pattern are not structured to resist curling in eitherdirection caused by shrinkage of the grout lines during curing. Thus,the straight grid tile pattern has two axes of weakness.

An improved tile pattern is an offset or staggered grid wherein thetiles are staggered in alternate rows, like bricks in a horizontal wall.With the tiles in this staggered grid pattern, the grout lines extendcontinuously only in one axis, rather than in two axes as with thestraight grid pattern described above. In addition, in the staggeredgrid pattern, the grout lines meet only at "three-way" intersectionsrather than four-way intersections as in the straight grid pattern.Consequently, the grout lines can shrink from only one direction as thetiles block off shrinkage from one side. The staggered grid pattern hasonly one "weak axis" i.e., along the uninterrupted grout lines, whereasthe straight grid pattern has two weak axes. The tiles in the staggeredgrid pattern reduce curl and also make a stronger layer by distributingweak points.

The relatively long grout lines extending in a single direction in thestaggered grid pattern can shrink substantially but still cannot causethe plane of the layer to bend upward, as the alternating tiles are ableto resist bending.

As the building material is cured, using preferred materials (XB 5081),there is a delay of approximately 2-3 seconds prior to shrinkage of thematerial. Consequently, if no grout is used, the tiles can be formed asfast as possible. However, in embodiments which include grout, the tilesmust be cured first and allowed to shrink (for a few seconds) prior tolaying grout. Tiles can be cured by skinning. This skinning can beformed using multi-pass, weave, rivets, as well as other techniquesdiscussed previously or discussed in previously incorporatedapplications. These curl reduction techniques allow the tiles to belarger in size without incurring significant curl. The tiles can becured by providing skin fill over the entire tile surface and thenmoving on to the next tile. Alternatively, the tiles can be partiallycured (e.g., a one line trace) followed by partial curing of othertiles, and then returning one or more times to fully cure the previouslypartially cured tiles.

In the staggered grid pattern, curing of the grout lines extendingunbroken in the x direction also causes shrinkage in the y directioninducing some amount of y direction curl. Triangles are another patternshape which can be used in tiling. These patterns can be replicatingtriangle patterns using a single triangle size and shape, or areplicating pattern using triangles of different shapes. In addition,patterns of random triangles can also be used, so long as adjacent edgesmatch to create an acceptably narrow gap. With patterns of randomtriangles, the grout lines can all be made short and interrupted so asnot to create any weak axes.

The hexagon is the most preferable tile shape. Hexagons can be closepacked to form solid tiles separated by thin isolating lines. A patternof hexagon tiles has no weak axis and no long grout lines. Following thehexagon tile pattern (FIG. 17a) in declining order of preference arerandom order and size triangles (FIG. 17b), higher order triangles (FIG.17c), staggered grid square tile patterns (brick wall) (FIG. 17d),straight grid tile patterns (FIG. 17e), square regular array oppositelypaired triangles (FIG. 17f) and square array regular triangle patterns(FIG. 17g). Other patterns besides those depicted in FIGS. 17a-g existwhich lead to regions of reasonably isotropic cure and no weak axisplanes (e.g. regions fitted by two or more types of polygons or closepacked circular tiles).

In forming layers with tiling, it is preferable to stagger the tilepositions from layer to layer, such that the tiles and adjacent layersdo not align with each other. Offsetting tiles between layers improvesstrength without unduly increasing curl. Tiles that are aligned ornon-staggered from layer to layer, (i.e., columns of tiles) may beacceptable for tiling in the first few layers above a down-facingfeature, followed by conversion to a method of building that connectsthe isolated tile regions together. However, if an entire object(excluding a down-facing portions of layer) is built with tiling,staggering of tiles between layers is desirable. The stagger can beintermittent, i.e., with groupings of short columns of tiles throughoutthe object. If grouting is provided, staggering of tiles between layersmay not be required for strength, but may be preferable for homogeneity.

A significant problem addressed by tiling is the need to reduce thelength of long vectors. Long vectors can cause tremendous amounts ofcurl if they are cured and adhered to a previous layer while they arestill shrinking. This stress-inducing adhesion to the previous layer canoccur along the length of the vector. In the case of a floating vector,it may occur where the ends of the vector attach to a boundary, if aretracted vector embodiment isn't being utilized.

An alternative approach for addressing this problem (which can beconsidered a derivative of tiling) is known as "Interrupted Scan". Inthis approach, vectors are drawn with periodic breaks along theirlengths. As with tiling, the exposed length is considerably longer thanthe gap between breaks. The breaks in the vectors can be in a randompattern over the length of a vector, or the breaks in neighboringvectors can form a random pattern. Alternative, and presently preferredmethods utilize breaks which are formed in a regular or at leastpredictable manner. The individual fragmented vectors can either becured to a depth to cause adhesion or they can be cured to a lesserdepth and thereby remain floating.

One method of implementing a form of weaved-interrupted scan is to scanwith a weave technique a first pass over a grid of tiles (the floatingpass) followed by a second pass over a second grid of tiles to completethe weave. The second grid of tiles is offset from the first grid. Thisis especially favorable when using a hexagonal tile pattern. To removethe possibility of favored axes, the hexagonal grid can be rotatedbetween passes as well as offset, or alternatively the hexagonal gridcan be rotated or translated from layer to layer.

FIG. 18a depicts a top view of cured material after a first pass over asquare tiling grid. FIG. 18b depicts the same top view after a secondpass over an offset square tiling grid. As can be seen in FIG. 18b, thisoffset-weaved tile pattern still potentially contains two weak axes.

FIGS. 19a, 19b, and 19c are similar to FIGS. 18a and 18b, but theyutilize a hexagonal tile grid. As can be seen in FIG. 19b, the hexagonaloffset-weaved tile pattern has no long straight weak axes. FIG. 19cdepicts an alternative offsetting technique wherein the hexagonal tilegrid is rotated as well as offset. Since the length and width ofhexagons are not equal, the method depicted in FIG. 19c does not form asimple recursive pattern.

Additional disclosure useful for implementing tiling is set forth inU.S. Pat. No. 5,321,622, which is incorporated herein by reference. Thisapplication discloses use of cross-sectional comparisons to determinedown-facing and other features associated with each cross-section. Thesetechniques can readily be extended to determine areas to be tiled. Theseareas to be tiled may include regions which are one or more layers abovedown-facing features. The most preferred method of implementing tiling,as well as other skintinuous methods disclosed herein, is throughdeviations between the object design or desired object design and thebuilding representation, where these deviations are incorporated by aSlice or Build type program. The modifications to the Slice program forimplementing tiling can include utilization of sets of alternatingclosely spaced and further spaced hatch paths. The area between theclosely spaced paths determines the grouting or gap regions whereas thearea between the further spaced paths determines the areas to be filed.A second preferred method is by formation of a vector set of skinningvectors which are continuous across the region which can be broken downinto portions of vectors to be cured and portions to be left uncured.This process of determining portions for curing and portions for notcuring can be made in the process computer as part of a Build program orthe like. Of course, other methods of implementation exist.

An additional method of improving stereolithographically produced partsis known as "Alternate Sequencing" or "Reciprocal Sequencing". Thistechnique is applicable to the various methods of skintinuous building,to the cross-hatched building styles, and to the original methods ofbuilding completely solid parts. In conventional stereolithography, thevector drawing sequence is substantially identical from layer to layer.This is especially true when considering fill and hatch vectors. Thefilling vectors on each layer are processed according to the same rulesand output in the same order on every layer. For example, thisconventional approach may scan a first set of X-hatch vectors startingwith the X-hatch vector which is closest to the X-axis (and the origin)followed by scanning successive X-hatch vectors which are further fromthe axis. After all the X-hatch vectors are processed, then the Y-hatchvectors may be scanned starting with the Y-hatch vector closest to theY-axis (and the origin) and followed by those vectors which aresuccessively further away. This conventional approach leads to the samecuring and shrinking forces reinforcing each other as successive layersare drawn. This is especially true for identical or nearly identicallayers. Therefore, if there are imbalanced forces associated with aparticular order of curing, even if these forces are minor,reinforcement from layer to layer can eventually cause enough build upto induce significant levels of distortion in a part. This distortionmay be seen in a partially completed part as it builds up or it may beseen shortly after post-curing or after allowing the part to settleafter post-curing.

This problem is well known in the art. For example, some symmetricalparts tend to curl in the same region, for no previously explainablereason. An example of this is a part called a SLAB-6. This is a 6-inchby 6-inch by 1/4-inch tall square diagnostic part. On repeated buildingsof this part utilizing conventional sequencing rules, the same corner ofthe part tends to pull away from the supports. The primary differencebetween the corners of the part is in the order in which they areformed.

A solution to this problem is Alternate Sequencing. Alternate Sequencingis a method of scanning wherein the scanning pattern is intentionallyaltered from layer to layer thereby leading to more uniform dispersionof stresses that can build up during the curing process. The pattern ofalternate sequencing may be random or predictable. It may be periodic ornon-periodic.

Presently preferred stereolithographic apparatuses, in particular theSLA250 by 3D Systems, Inc. of Valencia, Calif., use a conventionalsequencing pattern. At present, the conventional sequencing patternscans all hatch and fill vectors on all Slice layers in the samesequence. For convenience of description, we assume the machine isoriented so that the front of the vat is considered South and the backof the vat is considered North, and while facing the front of the vatthe right side of the vat is East and the left side is West.Specifically in current SLAs, Y vectors are drawn first (they run northand south), starting at the East side of the vat and proceeding towardsthe West side of the vat. The X-vectors are drawn second (they run eastand west) and propagate from North to South. This drawing pattern isdepicted in FIG. 20 wherein the numbers 1 through 8 indicate the drawingorder of the vectors.

A first example of alternate sequencing uses X-hatch and Y-hatch whereinthe X-hatch vectors are scanned followed by scanning the Y-hatch vectorson a first layer and then scanning the Y-hatch vectors followed byscanning the X-hatch vectors on a second layer and repeating thispattern on alternating layers.

A second example expands the two-layer pattern of the first example intoa four-layer pattern. On the first layer, Y-hatch is scanned first fromEast to West followed by scanning the X-hatch vectors from North toSouth. On the second layer, Y-hatch vectors are drawn first from West toEast followed by scanning the X-hatch vectors from South to North. Onthe third layer, the X-hatch vectors are scanned first from North toSouth followed by scanning the Y-hatch vectors from East to West. On thefourth and final layer, before repeating the pattern, the X-hatchvectors are scanned first from South to North followed by scanning ofthe Y-hatch vectors from West to East. An example of this drawing orderfor the four characteristic layers of the pattern is depicted in FIG.21a to 21d, wherein the numbers 1 through 8 indicate the relativedrawing order of the vectors.

A third example is described by the following table and is depicted inFIGS. 22a to 22h, wherein the numbers 1 through 8 indicate the relativedrawing order of the vectors:

    ______________________________________                                        Example 3: An 8-Layer X/Y Reciprocal Sequencing Pattern                         FIG. #   Layer Number                                                                              Vector Type                                                                            Propagation Direction                         ______________________________________                                        22a    1           Y          East to West                                        X North to South                                                            22b 2 X South to North                                                          Y West to East                                                              22c 3 Y East to West                                                            X South to North                                                            22d 4 X North to South                                                          Y West to East                                                              22e 5 Y West to East                                                            X South to North                                                            22f 6 X North to South                                                          Y East to West                                                              22g 7 Y West to East                                                            X North to South                                                            22h 8 X South to North                                                          Y East to West                                                            ______________________________________                                    

Similar scanning patterns can be developed based on X/60/120 hatch, orother hatch and fill types and other alternative sequences will beapparent to those of skill in the art. Similarly, drawing order can bebased on part geometry, wherein a fixed drawing order can be used toemphasize or deemphasize the tendency of an object feature to curl ornot to curl along a particular axis. Alternate Sequencing is a powerfultool which leads to more uniform internal stress distributions, reduceddistortions during building, and improved overall part accuracy.

Presently, the most preferred building method is to use "STAR" WEAVE.This embodiment uses an X/Y WEAVE technique, wherein the WEAVE patternis STaggered from layer to layer utilizing the above described 8-layerpattern of Alternate sequencing along with the hatch vectors beingRetracted from the boundary at their termination points. These STARWEAVE parameters generically discussed previously are more specificallydiscussed below.

In conventional WEAVE, X and Y hatch vectors on the nth layer having acured linewidth, L, are drawn with their respective centerlines adistance H from the centerlines of their nearest neighbors. The curedlines are separated from one another by a distance S=H-L. On the nextlayer, the procedure is repeated with the centerline of a vector on the(n+1)th layer lying directly above the centerline of a correspondingvector on the nth layer. This procedure is then continued on all layers.The result is that at the intersections of the X and Y vectors, thedoubly cured points sit directly above one another and the spacesbetween the doubly cured points sit directly above one another. Thus,conventional WEAVE is analogous to building a wall with bricks stackeddirectly on top of one another. On the other hand, the method ofSTAGGERED WEAVE has the centerline of a given vector on the (n+1)thlayer offset or staggered with respect to the corresponding vector onthe nth layer. Furthermore, the amount of offset, from layer to layer,is approximately H/2. Thus, a doubly exposed point on the (n+1)th layeris positioned midway between the four neighboring doubly exposed pointson the nth layer. Therefore, STAGGERED WEAVE is analogous to building awall with the positions of the bricks offset from those on the previouslayer. When using WEAVE, with some photopolymeric resins, microcrackshave been observed between adjacent vector lines. These microcracks havebeen eliminated by use of STAGGERED WEAVE. Of course other patterns ofSTAGGERING are possible including for example 3 or 4 layer patterns.

The retracted hatch used with STAR WEAVE involves drawing vectors sothat each is attached to only the border at its initiation point, and isretracted by a small distance, R, from the border on its opposite ortermination end. The optimum retraction distance may be buildingmaterial (e.g., resin) dependent but can readily be determined bybuilding several diagnostic parts with different amounts of retractionwith a given building material and thereafter determining whichretraction values are associated with the most accurately formed parts.Furthermore, the retraction itself should alternate between adjacentvectors and possibly between layers. For example, the first X vectormight be attached at a right border, and retracted by an appropriateamount (e.g., 0 to 50 mils, and preferably 15 to 30 mils, and morepreferably approximately 20 mils) from the left border. As previouslynoted, the adjacent vector (or some alternating pattern of vectors) willbe attached to the left border and retracted from the right border. Asimilar retraction technique is used for the Y-vectors. Advantages ofretracted hatch include reduced internal stresses during part building,reduced stresses on supports with a corresponding reduction inlikelihood of catastrophic support failure, reduced time dependent afterpost-cure distortion, known as "creep", and improved overall partaccuracy.

A main thrust of several of the above mentioned embodiments is achievingmaximum solidification with minimum distortion prior to attachment ofadjacent layers. Complete unattachment for too long a period of time canlead to drifting of solidified material out of its designated position.One method of maintaining the positioning of floating solidifiedmaterial without inducing curl into a preceding layer is to attach onlyone point of each vector (e.g., one point of each hatch vector of thefirst pass of hatch when using the weave approach) to the precedinglayer (which will tend to fix the vector in place). Then the one pointanchored vectors, which have been floating, are scanned by an additionalpass to complete the curing process and to insure adequate adhesionbetween boundaries and hatch.

Generically, multiscan techniques can be used with many of the aboveembodiments to help reduce curl. Multiscan may be done in the form ofmultiple passes over individual vectors or it may be done by crossing ofvectors or by riveting areas together, or the like.

The use of Smalleys and other curl reduction techniques may also bereadily used in conjunction with many of the above embodiments to reducevarious distortions.

An additional approach to minimizing curl in the various skintinuousembodiments is called "Strong Arm". In this approach the first layer ofan unsupported region is given extra cure to make it stronger andtherefore better able to resist the curl that the weaker, thinner upperlayers will attempt to induce in it.

Other distortion reduction techniques defined in the definition sectionof this application can also be used.

An additional aspect of the present invention involves improvedstereolithographic exposure techniques which involve a combination of afast shutter (e.g. an acousto-optic shutter) and creative scanningtechniques. This aspect of the present invention has several advantagesover the conventional scanning techniques of stereolithography: 1)improved generation of sharp object features, 2) ability to use lessexpensive scanners to generate high resolution parts, 3) improved partaccuracy by improved exposure, 4) smaller laser beam spot size at theworking surface, 5) longer scanner life time, and 6) improved partaccuracy by improved positional accuracy of a scanner-encoder system dueto more nearly constant mirror rotational velocities during partexposure.

Disadvantages of conventional stereolithography exposure systems involvelimited maximum angular acceleration of the scanning mirror systems. Thefirst disadvantage involves the inability to uniformly expose a line ofmaterial if the laser scanning system must accelerate or decelerateduring the exposure process. This need for acceleration during exposureand limits on the actual acceleration obtainable leads to a maximumscanning speed. This maximum scanning speed is based on the necessity ofmaintaining a relatively uniform exposure over the length of a vector,thereby limiting one to periods and lengths of acceleration that arerelatively short.

The second disadvantage with conventional scanning techniques involvesthe ability to form sharp features. When drawing sharp features with avector scanning system, the maximum angular acceleration capabilityand/or the ability of the servo/scanner system limits the accuracy ofthe sharp feature. These features exhibit some finite radius, andsometimes, some overshoot or ringing behavior beyond the sharp featurewhich corresponds to unwanted exposure. In order to limit theseinaccuracies, scanners with high acceleration capability must be used,and elaborate servo-drivers must be developed and optimized for bothregular and sharp feature performance. Higher acceleration scanningsystems are more costly and dual role servo optimization (for bothregular and sharp features) limits performance with regular features.

Spot size is also compromised as the rotating inertia (moment ofinertia) of the mirror must be reduced to maintain necessary systemacceleration capability. This precludes the use of larger mirrors withexisting scanners that would allow a larger beam size (smaller f/number)and allow a smaller focused spot size at the resin surface.

Scanner lifetime is also compromised by the peak bearing loads which aregenerated during these sharp-feature maneuvers.

A primary feature of this aspect of the invention involves shutteringthe beam when the beam needs to make a significant change in scanningdirection or velocity or needs to travel over a region which isn'tsupposed to be exposed. By shuttering the beam when these target pointsof non-exposure, change of direction, or change of velocity are reached,the scanning system is allowed to overshoot the target point anddecelerate or accelerate (including constant velocity changes ofscanning direction) while beyond the target point and outside the areato be exposed. After bringing the scanning system and therefore beam upto or down to the appropriate exposure speed along the appropriateexposure path and passing the beam across the target point the shutteris reopened so the beam can expose the working surface to properlyexpose the building medium.

A particular embodiment of this aspect of the invention involves thefollowing steps:

1) While drawing vector n, at a particular drawing speed and direction,evaluate vector n+1 to determine any necessary modifications to thescanning parameters that will need to be made. These scanning parameterchanges involve the determination of whether or not vector n and vectorn+1 meet head to tail, whether vector n and n+1 are to be exposedutilizing the same scanning speed, and whether or not there is a changein scanning direction between the two vectors which requires asignificant acceleration. If vector n and n+1 meet head to tail proceedto step 2a, if they do not meet head to tail proceed to step 2b.

2a) With regard to vectors that meet head to tail, an approximate laserpath radius at an up-coming sharp feature is computed. This computationmay involve the scanning velocity, or change thereof, and the change inscanning direction (angle). The purpose of the computation is to predicta radius based on the desire to keep potential scanning inaccuracies ata tolerable level. These inaccuracies include velocital inaccuracies aswell as positional inaccuracies at this junction.

3a) Determine whether the predicted radius is less than or greater thana preset maximum radius limit. If less than the preset radius limit thetransition from vector n to vector n+1 is made by the conventionalmethod of scanning. If the predicted radius is greater than the presetmaximum limit, the shutter is closed at the sharp corner junction. Andthe scanning system continues scanning across the junction in the samedirection as that scanned for vector n. While approaching the junctionor heading away from it a trajectory is determined which will bring thescanning direction and velocity in line with the desired scanningdirection and velocity for vector n+1. When the scanners repoint thebeam toward the junction point, while traveling along the desired pathat the desired velocity the shutter is opened and vector n+1 is scanned.The determined trajectory can be such as to minimize the arc of rotationwith which the beam would scan on the working surface if it were notshuttered.

4a. Continue this process by exposing vector n+1 and evaluating vectorn+2. Therefore in the above steps replace n+1 with n+2 and replace nwith n+1.

2b. With regard to vectors that do not meet head to tail, the shutter isclosed as the junction point is crossed. The scanning system continuesscanning across the junction in the same direction as that scanned forvector n. While approaching the junction or heading away from it, atrajectory is determined which will bring the scanning direction andvelocity in line with the desired scanning direction and velocity forvector n+1. When the scanners point the beam toward the beginning pointof vector n+1, while traveling along the desired path at the desiredvelocity the shutter is opened and vector n+1 is scanned.

3b. Continue this process by exposing vector n+1 and evaluating vectorn+2. Therefore, in the above step replace n+1 with n+2 and replace nwith n+1.

FIG. 25a to 25g depict various orientations of vector n and vector n+1,900 and 904 respectively, along with shuttered (virtual) scanning pathswhile maintaining a constant scanning speed and implementing a maximumtolerable acceleration which is indicated by 908. Alternatively theseshuttered paths 912 can be modified by allowing for a change in scanningspeed before and after the change in scanning direction (angularacceleration of the beam on the working surface). The scanning speed canbe reduced after shuttering occurs and before the attempted angularacceleration and then increased prior to reopening the shutter. Asindicated this may allow for shorter virtual scanning paths by allowingfor a tighter turning radius. FIGS. 25a, b, c, and e depict constantspeed virtual paths for different types of junctions using a maximumallowed value of angular acceleration. FIGS. 25d and e depict virtualpaths wherein the scanning speed is linearly decelerated and acceleratedprior to the angular acceleration involved in changing directions(smaller turning radii). Alternatively, FIGS. 25d and e can be viewed asdepicting virtual paths in which there is a change in speed during thevirtual scan to accommodate a desired change in scanning velocitybetween the two vectors.

Other alternative approaches include:

1) Any combination of moves beyond the junction that reduce the maximummirror acceleration. For example, as indicated above, as a sharp featuregets sharper and approaches a 180 degree turn, the technique of constantvelocity and minimum turning may result in unacceptable time delays(e.g. FIG. 25e). Therefore a computationally more complex embodiment canbe implemented where there isn't an attempt to minimize the magnitude ofthe angular rotation. An example of this type of embodiment is depictedin FIG. 25g, wherein the virtual scan begins with a slight angularacceleration in the direction opposite to that which would directlybring the scanning path parallel to the appropriate direction. This typeof virtual scan is known as an "airplane style" turn. The benefit ofthis use of opposite angular acceleration is in the reduced scanningpath length and therefore reduced virtual scanning time. This airplanetype of turn is appropriate for scanning hatch and fill type vectorswherein there is a short gap between the vectors and a required 180degree turn.

2) Use of two-stage scanning, wherein coarse scanners are limited tosome preset acceleration, while limited range, fast scanners "sharpenup" the corners. Acousto-optic crystal modulators act as frequencycontrolled diffraction gratings, by varying standing waves within thecrystal, and as such can be used to deflect a beam slightly for fineposition adjustments or to deflect it sufficiently into a beam trap,thereby acting as a shutter. Therefore, a pair of acousto opticmodulators or the like can function as both shutters and fine adjustscanners. An example of another candidate for fine adjustment scannersare piezoelectric crystal mirrors that can be mounted in front of or onthe course of scanning mirrors.

Preferred Methods of Obtaining Uniform Exposure

Turning to FIGS. 1 and 2, it will be seen that multiple exposure ofboundaries 10, hatch lines 12, and skin fill 14 will likely cause curedepth variations as depicted in FIG. 2.

To obtain a smooth down-facing region, the net exposure over all thearea elements must be the same. While uniform cure depth is necessaryfor smooth down-facing features, it is not necessary to achieve smoothup-facing features. These up-facing features attain their smooth surfacefinish from the smoothness of the building material working surface(e.g. resin surface), and from adequate strength of skins preventingtheir collapse from various forces including shrinkage duringpost-curing.

There are three main approaches that are exemplified herein to attainuniform exposure, particularly of down-facing regions. While the thirdapproach is most preferred, the other two are within the scope of theinvention, as are variations of all three that will be apparent to oneof ordinary skill in the art in light of the following description.

A first approach to avoid differential exposure is to avoid the use ofboth boundary and hatch vectors, and only use fill vectors to curedown-facing regions, using uniformly exposed skin fill that results inan appropriate skin depth. This is a viable method of obtaining uniformexposure and therefore cure depth, but can suffer from distortionproblems, as a relatively rigid frame (boundary and cross-hatch) isgenerally required to keep the skin from distorting as it is drawn. Asdescribed previously, if special attention is paid to the drawing orderof the vectors, this method can be made viable.

A second approach is to draw boundary and modified hatch vectors to thefull desired depth. First, hatch vectors must not be permitted to crossother hatch or boundary vectors to avoid extra depth being added tothese solidified crossover regions. The remaining pockets are filled inwith small skin fill vectors that do not cross any of the cured boundaryor hatch lines.

This second approach can be implemented, for example, by either of twomethods.

The first method is based on a single direction of hatch being drawn asuninterrupted vectors with hatch that runs in other directions "jumping"the points where they cross the first hatch type and where they crosseach other. These hatch vectors are broken into their requiredcomponents and stored in an output file for controlling the movement ofthe scanning mirrors (sometimes referred to as an .SLI file). Inaddition to hatch vectors that are drawn part of the time and jump theother part of the time, individual skin fill vectors can be created tofill each pocket that is formed by intersecting hatch and/or boundaryvectors. These fill vectors are stored in the .SLI file.

The second method is based on standard hatch and skin fill vectors beingstored in the SLI file along with a system (e.g., as part of the mirrordriving system) that uses slice, beam profile, vector intersectdirection, and cure depth parameters to break down vectors into drawingand jumping elements depending on whether they cross a hatch vector,boundary vector, or whether a hatch vector is underneath the vectorsbeing analyzed.

These two methods falling within the second approach require definitionof what it means for hatch and skin fill vectors to cross or lay on topof hatch or boundary vectors. This definition can be based on adetermination of how closely an exposed vector (both skin and hatch) canapproach a hatch or boundary vector without causing an increase inmaximum cure depth in that region.

The first method of this second approach may result in creating large.SLI files and large associated vector loading times. Accordingly, thesecond method of the second approach is currently more preferred, whenused in conjunction with a look-up table. The contents of such a tablein each instance will vary, depending upon the slice parameters used,beam profile characteristics, and desired cure depth to be obtained, andcan be routinely formulated for any required set of parameters by one ofordinary skill in the art. This system can optionally be adapted toaccount for approach angles between vectors.

The third, and currently most preferred, approach is based upon matchingskin parameters to hatch parameters, to avoid duplicate exposure by skinvectors of regions cured by hatch vectors. The duplicate exposure couldresult from skin vectors running parallel or antiparallel to the hatchvector regions.

While certain embodiments of this aspect of the invention have beenpresented other embodiments will be apparent to those of skill in theart after reviewing and understanding the disclosure herein. Thisapproach differs from the above-described approaches in that the skinvectors are drawn over the cross-hatch, giving additional exposure tohatch vectors that are not parallel to the skin vectors as drawn. Thiscontinuation of skin fill vectors will keep the .SLI file size frombecoming too large. This approach is collectively illustrated in FIG. 3.It will be noted that the skin fill in FIGS. 3c and 3d is discontinuousin areas corresponding to the x- and y-hatch running parallel thereto.The uniformity of the resulting cure depth is illustrated in FIG. 4.

A down-facing skin area, or "region," can be divided into categories or"subregions," based upon the nature of the exposure, i,e., whether andto what extent there is overlap between different vector exposures, asfollows:

subregion 1--skin exposure only;

subregion 2--skin and hatch overlapping exposure;

subregion 3--skin and boundary overlapping exposure;

subregion 4--hatch and boundary overlapping exposure;

and subregion 5--skin, hatch and boundary overlapping exposure.

Several approaches are suitable for exposing subregions 1 through 5 suchthat each region will be given the same net exposure. In the presentlymost preferred embodiments, three criteria are paramount.

First, to provide a suitably rigid frame to support the skin fill, thefollowing drawing order is preferred: first, boundary vectors, thenhatch vectors, and finally fill vectors are drawn.

Second, the fill vectors and the hatch vectors preferably begin and endshort of the boundary vectors by 1/2 the ECW of the boundary vectors(taking into account the angle of approach). This reduces subregions 3,4, and 5 to regions that contain boundary vectors only, such that theboundary vectors should be given the full exposure required in order toattain the desired cure depth.

Finally, a set of fill vectors are preferably drawn parallel to eachtype of hatch vector used, and all fill vector types are preferablygiven the same exposure, with the exception that fill vectors should notbe allowed to contribute to further exposure in the regions exposed bytheir parallel hatch type. For example, if x- and y-hatch are used, thenx- and y-fill are also used. Also x-fill vectors will only be createdthat are spaced at least 1/2 the ECW of the hatch lines away from thex-hatch vectors. A similar relationship should be maintained for y-filland y-hatch.

This means that subregion 1 will have an exposure equivalent to thecombined exposure of each fill type. Using the same example of x- andy-hatch and fill, each fill type should be exposed to 1/2 the exposurerequired to obtain the desired cure depth. Limiting fill vector exposurein this manner has a profound effect on subregion 2, which can beconsidered to consist of two microregions: a) a microregion containingoverlapping of the various hatch types as well as the various filltypes, and b) a microregion containing a single hatch type and thevarious fill types. Fill vectors will be absent from this firstmicroregion since they have been excluded to avoid re-exposing hatchedareas. Accordingly, the first microregion receives its total exposurefrom that of the combined hatch types. Thus, for x- and y-hatch, eachhatch type will contribute 1/2 the needed exposure. For the secondmicroregion, part of the exposure will be provided by the single hatchline, and the remainder by fill types that are nonparallel to it. Thisresults in the total exposure being given by the exposure of one hatchline plus the exposure from all but one of the skin types. Therefore,the number of exposure sources is equal to the number of cross hatchtypes, and hence, to the number of skin fill types. Using x- andy-hatch, for example, 1/2 the exposure in a region of x-hatch isprovided by this hatch and the other 1/2 is provided by the y-fill andvice-a-versa.

This most preferred approach can be summarized as follows: The preferredcuring order begins with boundary vectors, followed by hatch vectors,and finally by fill vectors. The boundary vectors provide the desiredcure depth. The skin and hatch vectors are shortened due to the ECW ofthe boundaries (shortened by the EEP). The fill vectors are not allowedto contribute to the exposure (be created) within 1/2 the ECW of eitherside of a parallel hatch vector. Each combination of hatch type with itsparallel skin type is used to achieve a uniform cure depth. Each hatchvector and net exposure of its corresponding fill type is given the sameexposure. Therefore, the individual fractional exposure (IFE), adimensionless fraction of the needed exposure, given to each type is thereciprocal of the number of different hatch types (NHT), i.e.,

    IFE=1/NHT.

A preferred embodiment of the above is based on the use of the presentlypreferred cross hatching method. This preferred hatching techniqueutilizes x and 60/120 hatch instead of x- and y-hatch. While theforegoing discussion relates to generally preferred methods of reducing"waffle" appearance, it is most preferred to use this method of wafflereduction/removal in connection with these presently preferred hatchtypes, i.e., equally-spaced x, 60° and 120° hatch. The resulting hatchvectors form equilateral triangles. Accordingly, there will be regionswhere there is one hatch vector, and regions where three hatch vectorsoverlap, but never, assuming accurate scanning, regions where only twovectors overlap. The corresponding skin fill will be in the X, 60°, and120° directions. These fill vectors will again not be allowed to produceadditional exposure within the 1/2 the ECW of either side of theirparallel hatch vectors and within 1/2 the ECW (taking into account theangle of incident) of the boundary vectors. The order of curing willagain be boundaries first then hatch and then fill. The boundaries willbe given a full exposure to bring them to the desired cure depth. Thehatch and fill vectors will again be shortened on each end by the EEP ofthe boundary vectors. The hatch vectors will each be given 1/3 therequired exposure necessary to achieve the final desired cure depth. Thefill vectors will be scanned such that the net exposure in the "skinonly" region will also be given by 1/3 of this exposure.

Except in regions of boundary vectors, to reach full exposure, eachpoint must be scanned by three vector types of 1/3 exposure from eachtype. In the region of skin alone, if all three skin types of equal(1/3) and overlapping exposures are used, a net exposure of 1 will beattained. Similarly, for a region of hatch and skin, one hatch type isused, along with the two skin types not parallel to it. Each is given anequal exposure of 1/3 to obtain a region of net exposure 1. If the hatchvectors form equilateral triangles, it follows that each time any twohatch vectors overlap, the third hatch vector will also be present. Ifeach hatch vector is given an exposure of 1/3, then the net exposure inthis region will be 1.

In regions where boundaries occur, an imbalanced situation exists due tothe presence of a boundary vector as well as the other vector typesdescribed above. The possibilities include the presence of: 1 boundary+3hatch vectors; 1 boundary+1 hatch+2 fill vectors; or 1 boundary+3 skinvectors. These combinations can be addressed, for example, in one of twoways: 1) have all hatch and fill vectors stop short of the boundary (at1/2 the effective cure width) and then give the boundary itself anexposure of one; or 2) select two of the hatch types and the same twoskin types to cure completely up to the boundary and stop the otherhatch and skin type short of the boundary at 1/2 the ECW of theboundary. If the boundary vectors are given a 1/3 cure, as are the othervectors, this combination results in a net exposure of 1 in the boundaryregion. The first of the above two options is presently the mostpreferred.

Yet another embodiment is based on the use of x and y hatch along withthe second option described above. In this case, the exposure in theboundary region would be due to the boundary vectors, one hatch and itscorresponding fill type with the other hatch and fill type stoppingshort. This embodiment has the advantage of insuring better adhesionbetween the boundary vectors and the fill and hatch vectors.

Still another embodiment is based on the use of x and 60/120 hatch alongwith the net exposure in the boundary areas being made up of exposingboundary vectors along with exposing two of the three types of hatch andthe corresponding fill vectors.

Other additional embodiments are conceivable. For example, a differentcure may be given to a hatch type and its corresponding fill type ascompared to the exposure given to the other hatch and fill types,wherein the net resulting exposure still produces the desired skindepth. It is also possible to extend this approach to include othersources of print through, such as that due to crosshatch from the layerabove the one that contains the down-facing feature. The cross hatch onthis higher layer can actually print through the lower layer. Using aparticular material, this print through effect is reduced when largerlayer thicknesses are used and increased when smaller layer thicknessesare used. Using experimental or analytical methods, the amount of printthrough can be determined, and the cross hatch on the layer containingthe down-facing feature can be given a correspondingly lower cure. Afterthe exposure of this layer and the following layer, the down-facingfeature will have a uniform cure. In most cases, there are crosshatchvectors on the layer immediately following the down-facing feature wherethe above compensation method would be useful. However, on rareoccasions, an up-facing feature may be on the same layer as adown-facing feature (therefore the feature is only one layer inthickness), requiring the hatch and fill to be perfectly matched basedon the one layer thickness of cure. On layers that have both up- anddown-facing features in the same area, it is important to ensure thatonly the down-facing skin is cured, so as not to use more exposure thandesired.

In the above description, only one effective cure width has beenexemplified to describe the proximity with which vectors can approachone another, but more than one ECW and EEP can be used in appropriatecircumstances.

The methods described herein have been implemented and verifiedexperimentally using x- and y-hatch and fill without need of modifiedsoftware. An object can be sliced using x- and y-hatch and x- and y-skinfill. The SLI file created can then be edited by hand, removing the skinfill vectors that are within a specific distance of their parallel hatchvectors (this distance is the ECW). This SLI file can then be mergedwith a support file. The range file can then be prepared giving an equalcure to the x- and y-hatch, and an appropriate single line exposuregiven to the fill vectors in order to produce an equivalent totalexposure as that from the x and y hatch.

Alternatively, the software can be modified:

1) by creating a skin type corresponding to 60° cross hatch and anothercorresponding to 120° cross hatch,

2) by creating a Slice option (or in some other appropriate program) toallow an offset for skin vectors to not be produced (or not drawn) inthe vicinity of hatch paths, and

3) creating an option to allow retraction of cross hatch and fillvectors on each end by a required amount.

Another preferred embodiment of the portion of the present inventiondealing with obtaining uniform skin depth is based on the idea of usingthe same exposure for both the hatch vectors and the skin vectors. Thehatch vectors and skin vectors are drawn at the same scanning speed. Inthe previous embodiment, the net area exposures were the same--not theindividual vector exposures. In this embodiment there is no need toproduce separate crosshatch. Instead, periodically spaced skin vectorsare pulled from the skin list and put into a hatch list for exposureprior to exposing the remaining skin vectors. These initially exposedskin vectors function as crosshatch and as such this method no longerrequires the computation of the ECW for crosshatch and skin vectors. Forthe hatch vectors to have adequate strength in order to form a frame forsupporting the skin vectors, it may be useful to space the skin vectorsat a maximum spacing (but still able to form an adequately uniform curedepth) so that the individual skin/hatch vectors will be relativelystrong.

Preferred Methods of Selecting and Determining Cure Depth

To make a theoretical determination of skin thickness, by one or moremethods of calculation, one would ordinarily consider the parameters ofvelocity [step period (SP) and step size (SS)], laser power, beamprofile, building material, working curve cure depth and associatedmaximum cure width, and vector offset. However, if a skin is formed thatis several times wider than the laser beam, and a step size and anoffset are used that are several times smaller than the laser beamwidth, the energy distribution over the skinned area will besubstantially uniformly distributed. If the energy is uniformlydistributed, the area will be uniformly cured to a particular depthdepending on the exposure. Thus, the exposure is defined as, Energy perunit area=Laser Power×Step Period/(Step Size×Offset). This aboverelationship can be equated to a particular thickness by plottingthickness versus log of exposure which, if the resin absorption obeysBeer's law will result in a linear relationship. From this relationship,one can determine the slope and intercept of this plot. Since the aboverelationship does not explicitly contain focus, profile, and machineworking curve parameters, the constants determined for one machineshould be directly usable on another machine as long as the parametersof material, wavelength, and distance from the scanning mirrors to thesurface of the resin are the same (or accounted for).

The foregoing detailed description and following Examples should beunderstood as being illustrative rather than limiting, as routinevariations and modifications are within the scope of the invention aswill be appreciated by one of ordinary skill in the art. Accordingly, itis intended that the invention be limited only by the appended claims,and all equivalents thereof.

EXAMPLES Example I

An experiment was conducted to determine whether skinning every layer ofa part gives any advantage with regard to minimizing distortion ascompared to building techniques based on trapping substantiallyuntransformed material within the limits of the part.

In this experiment, eight parts were built, in groups of two. Each groupincluded an object built on an elevator platform in front of themidpoint of the platform and an object built on the elevator platformbehind its midpoint, the objects were identical except for theirlocations on the building platform. A sample object is depicted in FIG.12. Each object was a one inch cube with no top and no bottom but with awall thickness of 100 mils. Various slicing and merging options wereused to create four different groups:

    ______________________________________                                        Grp Name                                                                             Description                                                            ______________________________________                                        Skntin01 -                                                                           Front object has skin on every layer.                                                Rear object has skin only on top and bottom layers.             Skntin02 -                                                                           Front object has skin only on top and bottom layers.                                 Rear object has skin on every layer.                            Skntin03 -                                                                           Front object has skin on every layer                                                 Rear object has skin on every layer.                            Skntin04 -                                                                           Front object has skin only on top and bottom layers.                                 Rear object has skin only on top and bottom layers.             All (8 parts) 4 groups were built with the following parameters:                        Layer thickness - 20 mils                                             Cure thickness for layer boundaries - 26 mils                                 Cure thickness for layer hatch - 26 mils.                                     Hatch vectors ran parallel to the x-axis and the                              y-axis spaced at 50 mils and skin                                             vectors ran parattel to the X-axis.                                         ______________________________________                                    

Cure thickness for skin fill was not specified as thickness but as 1/2the step period (SP) for a 26 mil cure (with an SS of 2) and step size(SS) of 16. All skin fill vectors ran parallel to the x-axis with a 2mil offset between them. (As a side note, measurement of skin thicknessunder similar cure conditions indicated that the cure thickness wasapproximately 20 mils. The building material was SLR 800, manufacturedby DeSoto Chemical.)

Measurements were made on each part to determine the resultingstructural accuracy of the part. No attempt was made to compensate forcure shrinkage.

A series of measurements were made near the top of each part. Themeasurements are depicted in FIG. 13. They are labeled 501 to 506.Measurements 501 to 503 measure distances parallel to the X axis, whilemeasurements 504 to 506 measure distances parallel to the Y axis. Theamount of distortion of the part along the X-axis is defined as

    Distortion (X)=(501+503)/2-502,

similarly distortion along the Y-axis is defined as

    Distortion (Y)=(504+506)/2-505.

The parts were skinned in the X-direction, the X-distortion is thedistortion of the wall perpendicular to the skinning direction and theY-distortion is the distortion of the wall parallel to the direction ofskinning.

The results are summarized as follows:

    __________________________________________________________________________    Skntin01 -                                                                         Front Object, all layers skinned along the X-direction                              distortion of watt perpendicular to direction of skinning =                   3.6 mils                                                             distortion of watt parallel to direction of skinning = 9.4 mils             Rear Object, Standard building, skinned only top & bottom                                distortion of watt perpendicular to direction of skinning =                   9.6 mils                                                             distortion of watt parallel to direction of skinning = 9.7 mils             Skntin02                                                                           Rear Object, all layers skinned along the X direction                               distortion of watt perpendicular to direction of skinning =                   1.2 mils                                                             distortion of wall parallel to direction of skinning = 8.2 mils             Front Object, Standard building, skinned only top & bottom                               distortion of watt perpendicular to direction of skinning =                   9.1 mils                                                             distortion of watt parallel to direction of skinning = 7.0 mils             Skntin03                                                                           Rear Object, all layers skinned along the X direction                               distortion of watt perpendicular to direction of skinning =                   1.5 mils                                                             distortion of watt parallel to direction of skinning = 7.9 mils             Front Object, all layers skinned along the X direction                                   distortion of wall perpendicular to direction of skinning =                   2.0 mils                                                             distortion of wall parallel to direction of skinning = 7.7 mils             Skntin04                                                                           Front Object, Standard building, skinned only top & bottom                          distortion of wall perpendicular to direction of skinning =                   11.0 mils                                                            distortion of wall parallel to direction of skinning = 9.7 mils             Rear Object, Standard building, skinned only top & bottom                                distortion of wall perpendicular to direction of skinning =                   9.5 mils                                                             distortion of wall parallel to direction of skinning = 7.9 mils             __________________________________________________________________________

In summary, skinning each layer in the x-direction reduced distortion indimensions measured parallel, but not perpendicular, to the X-axis.

Example II

In a second experiment, parts were built by skinning each layer withskin that was perpendicular to the direction of the skin on the previouslayer. In other words parts were built with X-type skin fill on everyother layer and Y-type skin on the other layers. The parts were the sameas those described for Example I, except for the differences inskinning.

    ______________________________________                                        Skntin05                                                                           Front Object, Every layer skinned, alternating X and Y types                     Distortion (X) = 4.9 mils                                               Distortion (Y) = 4.4 mils                                                   Rear Object, Standard building, skinned only top & bottom                             Distortion (X) 4.0 mils                                                 Distortion (Y) 5.3 mils                                                     Skntin06                                                                           Front Object, Standard building, skinned only top & bottom                       Distortion (X) = 3.1 mils                                               Distortion (Y) = 7.4 mils                                                   Rear Object, Every layer skinned, alternating X and Y types                           Distortion (X) = 5.0 mils                                               Distortion (Y) = -2.7 mifs                                                  Skntin07                                                                           Front, Standard building, skinned only top & Bottom                              Distortion (X) = 5.3 mils                                               Distortion (Y) = 6.2 mils                                                   Rear, Standard building, skinned only top & Bottom                                    Distortion (X) = 9.4 mils                                               Distortion (Y) = 6.8 mils                                                   Skntin08                                                                           Front Object, Every layer skinned, alternating X and Y types                     Distortion (X) = 2.5 mils                                               Distortion (Y) = 3.0 mils                                                   Rear Object, Every layer skinned, alternating X and Y types                           Distortion (X) = 1.9 mils                                               Distortion (Y) = 4.1 mils                                                   Skntin09                                                                           Front Object, Skinned on every layer, all skin of the Y-type                     Distortion (X) = 6.0 mils                                               Distortion (Y) = 1.0 mils                                                   Rear Object, Skinned on every layer, all skin of the X-type                           Distortion (X) = 1.5 mils                                               Distortion (Y) = 7.5 mils                                                   ______________________________________                                    

In summary, this data has substantial scatter but one can conclude thatskinning in x- and y-directions on opposite layers appears to generallyreduce distortion to some extent in each direction.

Example III

Similar experiments to those set forth in Examples I and II tended toshow that providing both x- and y-skin fill on each layer generallyreduced distortion in both x- and y-directions.

Similar experiments to those set forth in Examples I and II showed thatproviding X-skin fill along with X, 60, and 120 degree hatch on eachcross-section substantially reduced distortion in both directions.

Example IV

Four 1"×1" squares were built in a single build process on astereolithographic apparatus. Each square consisted of six 20 millayers. The structural support for each layer was based on x- andy-cross hatch, spaced at a 50 mil separation. Each square was supportedby a grid of webs placed at a spacing of 1/4". The webs consisted of ten20 mil layers. On the top surface of each square a standard skinningtechnique was applied. Therefore, the top surface was given x skin fillspaced at 2 mils on top of a grid of x- and y-crosshatch. The supportingweb structures were numbered 1 through 4 while the square patches werenumbered 5 through 8 (based on the merge order).

On the first layer of each square, x- and y-hatch were applied using aparticular exposure along with a particular skinning technique andassociated exposure. The second through sixth layers were given thestandard 26 mil cure depth for boundaries and hatch. On the first layerthe boundary vectors were given the full desired cure depth, withoutfactoring in any reduction in hatch and skin vectors for the purpose ofminimizing multiple exposures in boundary regions. The skinning/exposuretechnique was varied for the first layer of each patch.

Square Patch 5: "Standard Approach to Down-Facing Skins"

boundary=26 mil cure (SP 65, SS 2)

x- and y-cross hatch=26 mil cure (SP 65, SS 2)

x-skin fill=half the SP of a 26 mil exposure if SS=2 (SP 33, SS 16);fill vectors spaced at 2 mils with no gaps except exact duplicates ofhatch.

y-skin fill=None

Square Patch 6: "Down-Facing Skins with Skin Slightly Under-Exposed"

x- and y-cross hatch=20 mil cure (SP 29, SS 2)

boundary=20 mil cure (SP 29, SS 2)

x-skin fill=SP for a 16 mil cure if SS=2 (SP 17, SS 16); fill vectorsspaced at 2 mils with vectors removed that are 2 mils and 4 mils fromparallel hatch vectors (this means the skin fil vectors that are closestto the hatch are 6 mils away).

y-skin fill=SP for a 16 mil cure if SS=2 (SP 17, SS 16); fill vectorsspaced at 2 mils with vectors removed that are 2 mils and 4 mils fromparallel hatch vectors.

Square Patch 7: "Down Facing Skins with Skin Exposure Closely Matched toCross Hatch Exposure"

boundary=20 mil cure (SP 29, SS 2)

x- and y-cross hatch=20 mil cure (SP 29, SS 2)

x-skin fill=SP for a 20 mil cure if SS=2 (SP 29, SS 16); fill vectorsspaced at 2 mils with vectors removed that are 2 mils and 4 mils fromparallel hatch vectors.

y-skin fill=SP for a 20 mil cure if SS=2 (SP 29, SS 16); fill vectorsspaced at 2 mils with vectors removed that are 2 mils and 4 mils fromparallel hatch vectors.

Square Patch 8: "Down-Facing Skins with the Skin Slightly Over-Exposed"

boundary=20 mil cure (SP 29, SS 2)

x- and y-cross hatch=20 mil cure (SP 29, SS 2)

x-skin fill=SP for a 26 mil cure if SS=2 (SP 65, SS 16);

fill vectors spaced at 2 mils with vectors removed that are 2 and 4 milsfrom parallel hatch vectors.

y-skin fill=SP for a 26 mil cure if SS=2 (SP 65, SS 16);

fill vectors spaced at 2 mils with vectors removed that are 2 and 4 milsfrom parallel hatch vectors.

After building these four square patches they were examined, and none ofthe parts showed any signs of distortion. Part 5 had the typical largewaffle with cross hatch protruding beyond the skin. Part 6 had a smallerwaffle with cross hatch protruding beyond the skin. Part 7 had crosshatch and skin fill cured down to approximately the same level. However,there were slight protrusions along the sides of the cross hatch and aslight depression in the center of the cross hatch indicating that theskin was slightly overcured and maybe that the skin was not cured withinthe proper effective cure width of the cross hatch. Part 8 seemed tohave cross hatch whose center line was depressed as compared to the skinand to a raised overlapping edge where skin and cross hatch joined. Thesize of the discontinuities in Part 8 were larger than those in Part 7.See FIGS. 6a-6d for a sketch of each of these cases.

A scratch test indicated that Part 7 was almost smooth, Part 8 wasslightly rougher, Part 6 was much rougher, and finally Part 5 was theroughest of all. A visual inspection indicated that Part 7 looked best,followed by Part 8 or 6, then finally by Part 5.

The results of this experiment showed that the technique disclosedherein reduced waffle considerably. With the parameters used in thistest, hatch strength appeared to be sufficient to support the skinwithout distortion.

Example V

Experiments were done to test the usefulness of "Weave" for buildingparts without increasing the vertical distortion of the parts or theneed for adding additional supports.

In a first experiment 8 parts were built with the purpose of determiningthe most appropriate cure depths to use with the first pass ofcrosshatch in a weave building technique. The parts were built with 10mil layers, using XB-5081 stereolithography resin, with a HeCd laser of14.8 mW, and a beam diameter of 8.7 to 9.0 mils. The parts were builtwith boundaries and with X and Y hatch according to the "Weave"embodiment described earlier. That is, the spacing between crosshatchvectors was somewhat greater than the cure width associated with curingthe vectors. The boundary vectors were given a 16 mil cure and the curedepth for the first pass of the crosshatch was varied from part to part.Adhesion between layers was obtained by the overcure of the boundariesand the net cure depth (overcure) of the intersection points of 2equally exposed intersecting crosshatch vectors. The cure depths for thefirst pass of the crosshatch for different parts were 7, 8, 9, 10, 11,12, 13, and 14 mils. It was found that the parts that used initialcrosshatch exposures to obtain initial cure depths of 7, 8, and 9 milsshowed no sign of curl but they did demonstrate adequate adhesion. Theparts built with 10 mils and greater initial crosshatch cure depthdemonstrated unacceptable curl. Therefore, it is concluded that thefirst exposure of crosshatch in the preferred weave embodiment should bebased on a cure depth less than the layer thickness. It is possible thata cure depth somewhat greater than the layer thickness would beacceptable for certain materials that wouldn't show significant bondingbetween layers for small overcures.

A second experiment similar to the above was done to look at the mostappropriate hatch spacing to use with the "Weave" building method. Thematerial used was XB 5081, the layer thickness was 10 mils, the curedepth for boundaries was 12 mils, the cure depth for the first pass ofcrosshatch was 8 mils, and the beam diameter was 8.8 mils (maximum curewidth=10 mils). The hatch spacing for the different parts were 3, 5, 7,9, 11, 13, 15, and 17 mils. It was found that the parts built withspacings of 15 and 17 mils didn't have adequate structural integrity.The parts built with spacings of 3, 5, 7, and 9 mils showed unacceptablecurl. Finally, the parts built with a spacing of 11 and 13 mils (as wellas the parts built with spacings of 15 and 17 mils) showed no signs ofexcessive curl.

Example VI

An experiment was done to compare the post cure distortion of partsbuilt using the preferred "Weave" building method, the standard buildingmethod, and the standard spacing but staggered hatch building method.

This experiment consisted of building a series of parts with differentbuilding parameters. The parts were then cleaned and measured on acoordinate measuring machine (CMM). A first set of measurements measuredthe green (only partially cured) part. The parts were then identicallypostcured followed by another set of measurements of the parts on theCMM. This second set of measurements measured the fully cured part.

The parts used in this experiment are depicted in FIG. 15. FIG. 15adepicts two vertical walls built side by side with a small separationbetween them. The height of each wall 530 was 1.000 inch. The parts werebuilt and measured while attached to Web Supports that were attached tothe building platform (not shown). FIG. 15b depicts a top view of thetwo walls. The length of the walls 510 was 4.000 inches. The width ofeach wall 500 was 0.100 inches and the separation of the walls 520 was0.050 inches. Building two substantially back to back walls allowed eachwall to be post cured by synergistic stimulation coming fromsubstantially one side of the wall. This one sided curing results in apredictable nonuniform cure of the object and therefore results in apredictable direction of distortion. The measurements made by the CMM oneach wall are also depicted in FIG. 15b. Measurements 540, 550, 570, and580 were made at approximately 50 mils (0.050 inches) from the edge ofthe wall and approximately 100 mils below the upper surface of the wall.Measurements 560 and 590 were made along the same edge of the wall andapproximately 100 mils below the upper surface of the wall. Measurements560 and 590 were made along the same edge of the wall and at the samevertical position as measurements 540 and 550 and measurements 570 and580 respectively. They were made at the horizontal center of the edge ofthe wall.

FIG. 15c depicts distortion of the walls induced by post curing. FIG.15c depicts a top view of the walls. The dashed lines 600 and 610represent the desired shape of the walls, whereas the solid linesrepresent the actual shape of the walls. To determine the distortion ofthe first wall, the measurements of points 540 and 550 are connected bya straight line. The amount of distortion 630 is the length along theperpendicular distance between the line and point 560. To determine thedistortion of the second wall, the measurements of points 570 and 580are connected by a straight line. The amount of distortion 650 is thelength along the perpendicular distance between the line and point 590.

The parts were built with 10 mil layers on a standard SLA-250,manufactured by 3D Systems, using a HeCd laser and building material"XB-5081", manufactured by Ciba-Geigy. The post curing was done in a PCAusing 10-40 watt black light lamps (disclosed in U.S. patent applicationSer. No. 07/415,134). The cleaning of the parts was done ultrasonicallyin an alcohol bath for 2 minutes. Eight pairs of parts were built usingthe standard building technique (that is skinning only the up-facing anddown-facing features of the object along with using widely spacedcrosshatch to form the internal structure of the part). Four pairs ofparts were built using the standard building technique with themodification of staggering the hatch from layer to layer. Two sets ofparts were built using the weave approach.

It was found, from the green part measurements, that all the parts hadpractically no distortion after being removed from the vat and cleaned.The distortion of each part, at this stage, was less than 1 mil.Therefore to study post cure distortion we need only look at the postcure distortion data.

The results of the experiment are summarized below.

    ______________________________________                                        Building Method                                                                             Average Distortion                                              ______________________________________                                        Regular Hatch 12.52 mils                                                        Staggered Hatch 8.11 mils                                                     Weave 1.76 mils                                                             ______________________________________                                    

From this table we see that both the Staggered hatch and Weave buildingtechniques lead to a substantial decrease in post cure distortion. Weaveis seen to be especially useful for minimizing this distortion.

The automatic generation of vents and drains will now be described. Thetechnique involves utilization of the VIEW program, described in U.S.Pat. No. 5,182,715 (the '715 patent), which is incorporated by referenceherein as though set forth in full. Through VIEW, a user is able todisplay and possibly reorient an object prior to building it in order toobtain smoother surfaces and the like.

As described in the '715 patent, VIEW is configured to display arepresentation of the object in the .STL format. The .STL format is atesselated triangle format, in which the triangles substantially spanthe surface of the object, and each triangle is represented by its threevertices (in an exemplary embodiment, the three vertices are eachrepresented by three floating point numbers, and are ordered inaccordance with the "right-hand rule") and a normal vector (alsorepresented in an exemplary embodiment by three floating point numbersrepresenting the i, j, and k components of the normal). Additionaldetails about the .STL format are available in U.S. Pat. Nos. 5,059,359;5,137,662; 5,321,622; and 5,345,391, all of which are hereinincorporated by reference as though set forth in full.

As described in U.S. patent application Ser. No. 08/428,951, entitled"Simultaneous Multiple Layer Comparison", it is also possible to displayan object representation conforming to the .CTL format. As discussedtherein, the .CTL format provides several advantages relative to the.STL format which are relevant to VIEW. The first is that it facilitatesthe execution of scaling and rotation operations. The second is that,through appropriate selection of the delta value (the level ofacceptable rounding error), detail which is unnecessary from thestandpoint of VIEW can be eliminated, enabling the resultant object tobe efficiently displayed on relatively slow graphic display devices.

A first embodiment of an automatic method of adding vents and drains toan object involves displaying a representation of the object, whether inthe .CTL or .STL format, and automatically displaying to a user the flattriangles involved in representing the object. Only the flat trianglesare highlighted, since in this embodiment, a vent can only be placed ina flat up-facing triangle, while a drain can only be placed in a flatdown-facing triangle. VIEW is able to determine which triangles arecandidates for placement of a vent or drain through the normal vectorassociated with the triangle: the k component of the normal of all flattriangles is either 1 or -1, with the value of 1 being associated withup-facing triangles, and the value of -1 being associated withdown-facing triangles.

The process for creating vents involves the steps illustrated in FIG.28. In the first step, identified in the figure with numeral 1020, theuser selects the option of displaying a top view of the part. Using amouse, the user clicks on the "Top" button using the "ViewingTransformation" window provided by VIEW, which is illustrated in FIG.34. The "Viewing Transformation" window provides a user with thecapability to specify various characteristics about the display, such aswhether to transpose or rotate it in one or more coordinates, whether tozoom it, the perspective of the display (i.e., top, bottom, front, rear,right, light, isomorphic, or tessalated triangle), and the shading ofthe display. Examples of displaying a cube in which one or more of theseparameters have been varied are illustrated in FIGS. 31, 32, 33, and 35.

The next step, identified with numeral 1021 in FIG. 28, is to highlightthe candidate triangles in which a vent can be placed, which, asdiscussed, are the flat up-facing triangles. This step is accomplishedby clicking on the "Display Vent Triangles" bar provided in the "Ventsand Drains" window, both of which are illustrated in FIG. 30. As aresult of this step, the flat up-facing triangles are highlighted in thedisplay with a particular color, e.g., blue.

The next step, identified with numeral 1022 in FIG. 28, is to identifyselected ones of the flat up-facing triangles in which vents are to becreated. This is accomplished by moving the mouse arrow into any of thehighlighted triangles, and pressing one of the mouse buttons. Theselected triangle will then be highlighted in a different color (e.g.,white) than the other up-facing triangles. In this step, more than onetriangle can be selected.

The next step, identified with numeral 1023 in FIG. 28, is the automaticcreation of the vents. This is accomplished by clicking on the "Create"button displayed as part of the "Vents and Drains" window (illustratedin FIG. 30). The result is that a vent is created, using default values,in every one of the selected triangles. Simultaneously, as depicted bythe step identified with numeral 1024 in FIG. 28, the vents, and thetriangles in which they appear, are highlighted with an appropriatecolor (e.g., blue). All the other flat up-facing triangles areunhighlighted.

A vent which has been created in accordance with this process isillustrated in FIGS. 31-33 & 35 (the vent in all four figures isidentified with numeral 1032). As discussed, the four figures representdifferent perspectives and shading of the top of the object.

Also as discussed, in this embodiment, the vents, when first created,have a default shape and size. Advantageously, the default shape of thevent is a circle, but it should be appreciated that other shapes arepossible. Moreover, for the resins presently preferred for 3D Systems'commercial products (Cibatool SL 5170 for the SLA-190/250, and CibatoolSL 5180 for the SLA-500), it has been found that acceptable results canbe achieved with a default vent radius of 1.250 mm (0.05 in.).

The final step illustrated in FIG. 28 (the step identified with numeral1025) allows a user to change the default size of the vents, and alsoallows the user to move a vent (in the X-Y plane) or eliminate certainof the vents created in step 1023. To modify or change the size of avent requires the user first to select it. To select a vent, the usersimply positions the mouse arrow over the vent, and clicks the mousebutton. When selected, the vent will be highlighted using a particularcolor (e.g., white). The x,y,z coordinates of the vent, and the ventradius, will then be displayed in the appropriate data entry fieldswithin the "Vents and Drains" window. By entering new values in the xand y fields (the z field cannot be altered in this embodiment), theuser can change the location of the selected vent. To change the radiusof one or more selected vents, the user need only change the "VentRadius" field. When these new values are entered into the respectivefields, the display is automatically updated to reflect the changes. Byclicking on the "Clear" button, the user can deselect all selectedvents.

The process of creating drains will now be described. The process isvery similar to that of creating vents, with the major exceptions beingthat drains are typically larger than vents (since a drain, unlike avent, must be large enough to allow unsolidified material to flow), andare created on flat down-facing triangles as opposed to flat up-facingtriangles. Therefore, only the differences between this process and thepreviously-described process of creating vents will be described.

The process is illustrated in FIG. 29. The first step, identified withnumeral 1026, involves selecting a bottom view of the part using the"Viewing Transformation" window of FIG. 34. Next, in the step identifiedwith numeral 1027, the user selects the "Display Drain Triangles" buttonfrom the "Vents and Drains" window (FIG. 30). In response, VIEWhighlights the flat down-facing triangles using an appropriate color,i.e., yellow. In the third step, identified with numeral 1028, the userselects from the set of flat down-facing triangles, the desiredtriangles for the placement of drains. In response, VIEW highlights theselected triangles using an appropriate different color, i.e., white. Inthe next step, identified with numeral 1029, the user prompts VIEW toautomatically create the drains by clicking on the "Create" button inthe "Vents and Drains" window. VIEW does so by creating the drains usingdefault parameters in the selected triangles. Presently, the defaultshape, position, and size of a drain is a circle centered in the middleof the triangle having a radius of 3.750 mm (0.150 in.) for both theCibatool SL 5170 (preferred for use with the SLA 190/250) and SL 5180(preferred for use with the SLA 500). Next, in the step identified withnumeral 1030, VIEW highlights the triangles selected for placement ofdrains and the drains themselves with an appropriate color (i.e.,yellow), and unhighlights the other flat down-facing triangles. Finally,in the step identified with numeral 1031, the user optionallyrepositions, changes the radius of, or deselects any of the drains usingthe "Vents and Drains" window. The result is one or more drains asdepicted in FIGS. 31 and 32 (through identifying numerals 1033 and1034).

At present, through appropriate commands, VIEW allows a user to changethe default radius of the vents and drains and their positioning. Itshould be appreciated that the inclusion of additional commands arepossible which provide for a default shape. It should also beappreciated that several other refinements and enhancements of thisembodiment are possible, including, without limitation, the insertion ofvents or drains on near-flat surfaces.

After drains and vents have been inserted into the object representationas described, VIEW allows user to save the information descriptive ofthe drains and vents in a data file. At present, the information savedby VIEW consists of, for each vent or drain, the x, y, z coordinates ofthe center point of the vent or drain; the x, y, z components (I, j, k)of the triangle normal, and the radius of the vent or drain. To actuallybuild an object with the vents or drains inserted, the user inputs thisinformation into C-SLICE, i.e., the Boolean layer comparison SLICEprogram described in U.S. Pat. No. 5,321,622 (the '622 patent), alongwith the unaltered object representation. From the objectrepresentation, C-SLICE produces up to three types of boundaries inrelation to an object layer, up-facing boundaries (UB), layer boundaries(LB), and down-facing layer boundaries (DB). After producing thisboundary information, C-SLICE manipulates it based on the informationprovided by VIEW. For a given drain or vent, C-SLICE determines whichlayer is required to be modified using the z-coordinate of the trianglein which the vent or drain appears (the singular term "z-coordinate" isused given that the triangles in this first embodiment are constrainedto be flat triangles which, by definition, lie entirely within a givenz-plane). The sign of the k-component of the triangle normal is thenused to determine whether to modify the UB or DB information. If thesign is positive, indicative of a vent, the modification is made to theUB information; if negative, the modification is made to the DBinformation.

The modification made to this data will now be described. As discussedin the '622 patent, the UB and DB information created by C-SLICE ispreferably in the form of a polylist, i.e., an ordered sequence of linesegments which circumscribe a solid or hollow feature of the object.Advantageously, the order of the coordinates obeys the right-hand rule.In accordance with this rule, the segments are ordered in acounterclockwise direction if they define an exterior boundary of theobject, i.e., circumscribe a solid portion of the object. Conversely, ifthey define an interior boundary of the object, i.e., circumscribe ahollow portion of the object, the segments will be ordered in aclockwise direction.

The technique involves describing the vent or drain with a polylist. Inthe present embodiment, a polylist of 255 segments is used, but itshould be appreciated that other options are possible. Advantageously,the coordinates of the segments are ordered, in accordance with theright-hand rule, in a clockwise direction. That is because, bydefinition, they describe a hole. The sign of the k component of thetriangle normal is then evaluated. If the sign is positive, the UB datais earmarked for modification; if the sign is negative, the DB data isearmarked for modification. A Boolean union operation, as is describedin the '622 patent, is then performed between the appropriate data,whether UB or DB, and the polylist describing the hole or vent inquestion.

This step is illustrated in FIG. 36. The circle identified with numeral1035 depicts a polylist which is representative of a border (whetherup-facing or down-facing) enclosing solid area. In accordance with theright-hand rule, the segments making up the polylist are ordered in acounter-clockwise direction. The circle identified with numeral 1036, onthe other hand, depicts a polylist which represents a vent or drain. Inaccordance with the right-hand rule, the segments making up the polylistare ordered in a clockwise direction since a vent or drain by definitionencloses a hollow region. The Boolean union of the two polylists isidentified with numeral 1037.

An aspect of QUICKCAST, described earlier, is the creation of multiplelayers of skinning of the object in order to create a strong shell foruse in investment casting. The aforementioned step, in which thepolylist making up a hole or vent is Boolean unioned with UB or DB data,must be repeated for each of these skinned layers. If it is onlyperformed with less than all, the hole or vent will become skinned over,i.e., blocked, in the final part.

Once the appropriate UB or DB data has been modified, the C-SLICEprocess continues as is described in the '622 patent in combination withthe inventive concepts described herein in relation to the QUICKCASTstyle of part building. The result is a part built according to theQUICKCAST style in which vents or drains have been inserted into thepart.

It should be appreciated that this embodiment for automatic vent ordrain creation can also be used to drain unsolidified material fromtrapped volumes within solid parts. As discussed in U.S. Pat. No.5,258,146, which is hereby incorporated by reference herein as thoughset forth in full, trapped volumes can lead to leading and trailing edgeproblems due to the buildup of material during the recoating process.The problem can be significant: the buildup of material, oncesolidified, can interfere with the operation of the doctor blade orsweeper used to recoat. The selection of appropriate recoatingparameters to at least partly eliminate these problems, as discussed inthe previously-referenced U.S. Pat. No. 5,258,146, is not an entirelysatisfactory solution because it prevents the selection of recoatingparameters which are independent of the geometry of the particular partat hand. Automatic vent or drain generation would help eliminate trappedvolumes. In this technique, the union operation is not only performed ondown-facing or up-facing regions, but on all regions (downfacing,upfacing and continuing) on all layers between the specified down-facingor up-facing feature and the opposite up-facing or down-facing featureinclusive.

It should also be appreciated that there is no requirement in thepresent embodiment that vents or drains fit within a single triangle, oreven within a particular up- or down-facing region. If the vent or drainfalls partially outside of an up- or down-facing region, the vent ordrain will be reduced in size since part of it will be missing.

This phenomenon is illustrated in FIG. 37. As shown, polylist 1035,representing either an up-facing or down-facing border, is Booleanunioned with polylist 1036' which, as shown, encircles a hole which isnot entirely encompassed by the polylist 1035. The result of this unionoperation is the boundary depicted in FIG. 37. Since this boundarydefines the limits to which hatch or skin will be created on the layerin question, a vent or drain, identified with numeral 1039, will stillbe created in the final part, albeit with a reduced surface area inrelation to the hole described by polylist 1036'.

Several refinements or enhancements of this embodiment will now bedescribed. In one enhancement, the data provided by VIEW can be used incombination with an object representation formatted in accordance withthe SLC format (a contour/layer format described in the '622 patent).Through Boolean union operations, such data can be modified using thevent/drain data provided by VIEW in the manner described.

A second embodiment for automatically inserting vents/drains in athree-dimensional object will now be described. In this embodiment, thecapability is provided for introducing vents or drains in near-flatregions of the object, a capability which is especially useful in thecase of parts which, through reorientation to eliminate trapped volumes,facilitate the creation of supports, and the like, have no flat regions.

A first approach to implementing this second embodiment involvesintroducing a flat region into the object representation at theoriginally near flat region, and then applying the just-discussedembodiment to insert a drain or vent in the just-created flat region.The technique involves using VIEW to display the object, selecting froma library of predetermined representations a representation of a secondobject having a flat surface (such as a cylinder or rectangular bar),situating in VIEW the second object representation such that the flatarea is appropriately situated within the near-flat region of the firstobject representation, and then performing a Boolean differencingoperation between the two representations. The previously-discussedembodiment is then used to insert a vent or drain at the resultant flatarea created in the first object representation.

The technique is illustrated in FIGS. 38-39. In FIG. 38 is shown a nearflat area, identified in the figure with numeral 1040, and arepresentation of a cylinder, identified with numeral 1041, having aflat area 1042 which has been situated within the near flat area. Theresult of the Boolean differencing operation is shown in FIG. 39. Asshown, a flat region, identified with numeral 1043, is created withinthe part for insertion of vents or drains.

A variant of this technique involves performing this Boolean operationin the CAD system, i.e., modifying an .STL file representing the object.

A second approach to implementing this second embodiment involves amodification to C-SLICE, the Boolean layer comparison "slice" programdescribed in the '622 patent. A flowchart of the technique isillustrated in FIG. 40a. The first step, identified with numeral 1044,involves taking as input the preliminary boundary data described in the'622 patent (used as input to the Boolean layer comparison operationswhich result in the formation of the UB, LB, and DB data), i.e., theL[i] data, and performing a Boolean differencing between this data andthe data descriptive of desired vent and drain zones. The effect is tocreate a flat region for the insertion of a vent/drain. This step islustrated in FIG. 40b. There is shown the preliminary boundary data fora layer, identified with numeral 1057, which is moved/retracted toposition 1057', through this Boolean differencing operating. The effectis to create flat region 1058. In the second step, identified withnumeral 1045, the modified L[i] data is processed through C-SLICE in thetraditional way to arrive at UB, LB, and DB data reflecting theinclusion of the vent and drain zones. In the third step, identifiedwith numeral 1046, the resultant UB and DB data is modified through asecond pass with the data descriptive of the vents and drains in themanner described previously in relation to the first embodiment, i.e.creation of polylists descriptive of the vents/drains, followed aBoolean union between this data and the UB/DB data. This step isillustrated in FIG. 40c. There is shown the inclusion of vent/drain 1059in the flat region 1058 created in step 1044. This modified data is thenused to form the part.

A potential problem with these approaches involves the possibleformation of relatively large indentations in the object due to the needto create a large enough flat region in order to insert a drain or ventof acceptable size. In particular, as the slope of the slanted surfacebecomes steeper it is clear that the indentation becomes larger for agien size of the flat feature to be created. The indentations thusformed may represent an unacceptable distortion of the object surface.An additional potential problem with these approaches arises from thefact that the hole inserted is not located at the lowest extreme of theobject feature into which it is inserted. If the hole is to act as adrain, it is apparent that not all of the internal liquid can be drainedfrom the object unless the object is tilted. Of course, if an automaticobject tiling feature is added to the platform support structure towhich the object is attached, this becomes a non-issue.

These problems may be partially overcome by revising the embodiment sothat the hole exists in the vertical surface created by the section ofthe object that is Boolean subtracted. Techniques for implementingvertical holes are described hereinafter.

A third approach to implementing this second embodiment simply involvesremoving the skins associated with a sloped surface and leaving thelayer boundaries in place. In this case the defined hole would have aslanted orientation wherein portions of the hole would be associatedwith successive layers. The partial hole associated with the successivelayers or cross-sections of data can be obtained by projecting theportion of the slanted hole in between two cross-sections onto theappropriate of the two cross-sections (typically the upper portion ofthe layer or upper cross-section when forming a drain). Techniques forperforming the projection operation are described in previouslyreferenced U.S. Pat. Nos. 5,345,391 and 5,321,622.

A potential problem with this last approach is that it may not beeffective for purposes of inserting vents or drains into extremely steepnear-flat surfaces. In FIG. 41a, for example, a steep near-flat surface(identified with numeral 1047) is shown. The material solidified byexposure of the boundaries of the LB regions associated with therespective layers are identified with numerals 1049a, 1049b, 1049c, and1049d. The DB regions associated with the respective layers areidentified with numerals 1048a, 1048b, 1048c, and 1048d. The removal ofthe DB regions, which the above-described variant will accomplish, willleave no gap in the resultant surface of the object. That is because thesurface is so steep, that the LB regions from successive layers areclose enough to one another to close any gaps.

This approach, however, will be effective with more gradual near-flatsurfaces, such as that identified with numeral 1047' in FIG. 41b. Inthis figure, the material solidified by exposure of the boundaries ofthe LB regions for the respective layers are identified with numerals1049a', 1049b', and 1049c'. The DB regions for the respective layers areidentified with numerals 1048a', 1048b', and 1048c'. The removal of theDB regions in this case will leave gaps, identified with numerals 1050aand 1050b, which are not "plugged" by the remaining material solidifiedby exposure of the boundaries of the LB regions. Drains in these regionswould be effective for the purpose of draining unsolidified materialfrom the part. Consequently, it may be appropriate to limit applicationof this variant to gradually-sloping near-flat surfaces.

A fourth approach for implementing this second embodiment will now bedescribed. An advantageous aspect of this approach is that it can beused to insert vents/drains in vertical as well as near-flat regions.According to this embodiment, a new boundary type is created known asthe "anti-boundary." A requirement imposed by C-SLICE is that layerboundaries (LB) form closed loops. The requirement is imposed because ofthe function performed by layer boundaries: they are used to generatehatch and fill vectors. As illustrated in FIG. 42, if a break 1052 wereto appear in the layer boundary 1051 of an object, it would lead to thecreation of unwanted hatch or fill (identified with numeral 1053).

This requirement creates a problem for the creation of vents/drains insteep or vertical surfaces. As discussed, for these surfaces, the layerboundaries from successive layers are so close that they inhibit orprevent the creation of vents/drains through openings in skin fillalone. Thus, a means must be provided for the insertion of breaks intolayer boundaries.

The addition of temporary boundaries solves this problem. Temporaryboundaries define the portion of layer boundaries which are not to besolidified. They also complement regular boundaries so a complete closedloop is formed, but they are not included with the boundaries to beexposed.

An approach for generating temporary boundaries, illustrated in FIGS.43a-43b, is from the intersection between the desired vent/drain (as itexists on the near-flat/vertical surface of the object) (identified inthe figures with numeral 1054) and the slicing planes (identified inFIG. 43a with numerals 1055a, 1055b, 1055c, 1055d, 1055e, and 1055f)used in C-SLICE (layer comparison slice). The result is a series oflines (partial boundaries) at various z-positions, identified in FIG.43b with numerals 1056a, 1056b, 1056c, 1056d, and 1056e, whichconstitute the temporary boundaries. This approach would be effectivefor use with both the SLA-250 (in which hatch and fill are produced inC-SLICE at or about the same time as the layer boundary information),and the SLA-500 (in which hatch and fill are created "on the fly" (asdescribed in U.S. Pat. No. 5,182,715, which is incorporated by referenceherein as though set forth in full)). Both temporary and regularboundaries would be passed to the SLA-500, both for use in hatchgeneration, but with only the regular boundaries for use in exposing.

Alternatively, two boundaries can be formed, wherein one boundaryincludes a purposely designed break in it and is used for exposing thematerial. The other boundary forms a complete loop and is used for hatchor fill generation.

As a further alternative, a complete boundary loop can be generatedalong with one or more "anti-boundary" segments. In this case, thecomplete boundary loop is used for generating hatch after which aboolean difference is taken between the boundary loop and theanti-boundary segment to yield an incomplete or broken boundary to beutilized in exposing the material.

While several embodiments have been shown and described, it will beapparent to those skilled in the art that various modifications arepossible without departing from the spirit and scope of the invention.

Though the above embodiments have been primarily described in terms oftheir implementation in systems that operate based on the selectivesolidification of photopolymers (the preferred system), it is believedthat the data processing and object building techniques are applicableto other segments of the Rapid Prototyping and Manufacturing industryalone or in combination. These other segments include technologiesinvolving the selective solidification of polymerizable material by useof IR, visible and other forms of radiation or by the selectivedeposition of a medium onto the material (e.g. a photoinitiator beingdispensed onto a polymerizable material in a continuous or intermittentlight environment or selective deposition of the second part of atwo-part epoxy onto the first part). Also, technologies involved in thebuild of objects from selectively solidified powdered materials (e.g. bysintering or selective deposition of a reactive material or bindingagent) are included in these segments. Furthermore, technologiesutilizing the layer by layer build up of sheet material or the selectivedispensing of a material that solidifies when dispensed into anappropriate environment (e.g. the technologies disclosed in U.S. Pat.Nos. 5,192,559 and 5,141,680--which are incorporated herein by thisreference) are included in these segments.

I claim:
 1. A method for automatically inserting a drain or vent in athree-dimensional object representation to derive a modified objectrepresentation for subsequent use in constructing a three-dimensionalobject from a solidified medium, the object comprising at least oneobject region and at least one non-object region separated by at leastone surface of the object, comprising manipulating the representation toinsert the drain or vent through at least a portion of the at least onesurface so as to form a passage to connect the at least one objectregion to the at least one non-object region.
 2. The method of claim 1wherein the at least one surface is a flat surface.
 3. The method ofclaim 1 wherein the at least one surface is a sloped surface.
 4. Themethod of claim 1 wherein the at least one surface is a verticalsurface.
 5. The method of claim 1 wherein the manipulating of therepresentation comprises:taking as input an object representation whichcomprises a plurality of polygons which substantially span a surface ofthe object; and inserting the drain or vent in at least one selectedpolygon.
 6. The method of claim 5 wherein said at least one selectedpolygon is a flat polygon.
 7. A method for automatically inserting adrain or vent in a vertical or a sloped surface of a three-dimensionalobject representation, comprising:taking as input the three-dimensionalobject representation, which representation comprises a plurality ofboundaries of cross-sections of the object; taking as input datadescriptive of the drain or vent; and modifying at least one of saidcross-sectional boundaries by performing a Boolean operation betweendata descriptive of said cross-sectional boundary and said datadescriptive of said drain or vent.
 8. A method for automaticallyinserting a drain or vent in a sloped surface of a firstthree-dimensional object representation, comprising:supplying the firstobject representation, the first object representation having at leastone sloped surface; selecting a second object representation having atleast one of a vertical surface or a flat surface; relatively orientingthe first and second object representations such that the flat surfaceand/or the vertical surface of the second object representation issituated near the at least one sloped surface of the first objectrepresentation; performing a Boolean operation between the first andsecond object representations to form a modified first objectrepresentation, including a flat surface or vertical surface formed atthe at least one sloped surface; and inserting the drain or vent in theflat or vertical surface of the modified first object representation. 9.A method for automatically inserting a drain or vent in a surface of athree-dimensional object representation, comprising:taking as input thethree-dimensional object representation which comprises a plurality ofrepresentations of boundaries of cross-sections of the object; derivingat least one modified boundary representation comprising removing atleast a portion of at least one boundary representation comprising anintersection between the at least one boundary and a desired drain orvent.
 10. The method of claim 1 wherein the object representation isused in constructing the object from a solidifiable medium from aplurality of formed and adhered cross-sections, wherein at least somecross-sections of the object are formed only in part from solidifiedmedium, and wherein the solidified medium substantially bounds theobject region and forms a support structure internal to the objectregion.
 11. The method of claim 10 wherein the support structureinternal to the object region comprises a plurality of solidifiedelements at least partially spaced from one another by gaps ofunsolidified medium, and wherein unsolidified medium in the gaps is atleast partially removed through the drain or vent.
 12. The method ofclaim 2 wherein the flat surface is a horizontal surface.
 13. The methodof claim 6 wherein the flat polygon is a horizontal polygon.
 14. Themethod of claim 7 wherein the modified object representation is used inconstructing the object from a solidifiable medium from a plurality offormed and adhered cross-sections, wherein at least some cross-sectionsof the object are formed only in part from solidified medium, andwherein the solidified medium substantially bounds the object region andforms a support structure internal to the object region.
 15. The methodof claim 14 wherein the support structure internal to the object regioncomprises a plurality of solidified elements at least partially spacedfrom one another by gaps of unsolidified medium, and whereinunsolidified medium in the gaps is at least partially removed throughthe drain or vent.
 16. The method of claim 8 wherein the modified objectrepresentation is used in constructing the object from a solidifiablemedium from a plurality of formed and adhered cross-sections, wherein atleast some cross-sections of the object are formed only in part fromsolidifiable medium, and wherein the solidified medium substantiallybounds the object region and forms a support structure internal to theobject region.
 17. The method of claim 16 wherein the support structureinternal to the object region comprises a plurality of solidifiedelements at least partially spaced from one another by gaps ofunsolidified medium, and wherein unsolidified medium in the gaps is atleast partially removed through the drain or vent.
 18. The method ofclaim 9 wherein the object representation is used in constructing theobject from a solidifiable medium from a plurality of formed and adheredcross-sections, wherein at least some cross-sections of the object areformed only in part from solidified medium, and wherein the solidifiedmedium substantially bounds the object region and forms a supportstructure internal to the object region.
 19. The method of claim 18wherein the support structure internal to the object region comprises aplurality of solidified elements at least partially spaced from oneanother by gaps of unsolidified medium, and wherein unsolidified mediumin the gaps is at least partially removed through the drain or vent. 20.A method of constructing a three-dimensional object from a solidifiablemedium, comprising:supplying data descriptive of the object; forminglayers of unsolidified medium adjacent to previously formedcross-sections of the object in preparation for forming subsequentcross-sections of the object; selectively exposing the layers ofunsolidified medium to prescribed stimulation to selectively solidifyportions of the layers to form successive cross-sections of the object;automatically adhering the cross-sections together upon formation toconstruct the three-dimensional object cross-section by cross-section,the object comprising object regions and non-object regions separated bvsurfaces of the object; and leaving at least a portion of the surface ofthe object unsolidified to form a passage from the object region to thenon-object region so as to allow at least a portion of any unsolidifiedmedium within the object region to be at least partially removed throughthe passage, wherein the surface region remaining unsolidified resultsfrom the removal of surface data descriptive of the surface, and whereinthe medium is a liquid photopolymer, and wherein the passage isspecified on the surface by specifying a location and a passage size.21. The method of claim 20 wherein the passage size is selected from oneor more preset sizes automatically once the location is specified.